Docstoc

slides

Document Sample
slides Powered By Docstoc
					                     Introduction
     Visualization by Annotation
          Visualization Interface
                    Conclusions




Chapter 13: Visualization Techniques

                     Helmut Simonis

           Cork Constraint Computation Centre
             Computer Science Department
                 University College Cork
                         Ireland


          ECLiPSe ELearning                   Overview




                Helmut Simonis      Visualization Techniques   1
                                Introduction
                Visualization by Annotation
                     Visualization Interface
                               Conclusions


Licence



  This work is licensed under the Creative Commons
  Attribution-Noncommercial-Share Alike 3.0 Unported License.
  To view a copy of this license, visit http:
  //creativecommons.org/licenses/by-nc-sa/3.0/ or
  send a letter to Creative Commons, 171 Second Street, Suite
  300, San Francisco, California, 94105, USA.




                           Helmut Simonis      Visualization Techniques   2
                                     Introduction
                     Visualization by Annotation
                          Visualization Interface
                                    Conclusions


Outline


  1   Introduction

  2   Visualization by Annotation

  3   Visualization Interface

  4   Conclusions




                                Helmut Simonis      Visualization Techniques   3
                                Introduction
                Visualization by Annotation
                     Visualization Interface
                               Conclusions


What we want to introduce




     Why visualize?
     How to visualize constraint programs
     Visualization Interface
     Visualization Tool




                           Helmut Simonis      Visualization Techniques   4
                                     Introduction
                     Visualization by Annotation
                          Visualization Interface
                                    Conclusions


Outline


  1   Introduction

  2   Visualization by Annotation

  3   Visualization Interface

  4   Conclusions




                                Helmut Simonis      Visualization Techniques   5
                              Introduction
              Visualization by Annotation
                   Visualization Interface
                             Conclusions


Background


    Gift grant from Cisco Systems/Silicon Valley Community
    Foundation
    Cisco owns open-sourced ECLiPSe system
    How to expand user-base?
    Self-taught course in constraint programming
    Intended for Cisco engineers/programmers
    Open source/available to community
    Website
    http://4c.ucc.ie/~hsimonis/ELearning/index.htm



                         Helmut Simonis      Visualization Techniques   6
                                Introduction
                Visualization by Annotation
                     Visualization Interface
                               Conclusions


Format




    Video lectures
    Slides
    Handout
    Exercises




                           Helmut Simonis      Visualization Techniques   7
                                Introduction
                Visualization by Annotation
                     Visualization Interface
                               Conclusions


Problems Handled in Course




     Must have puzzles!
     Send+More=Money
     Sudoku
     N-queens
     Shikaku




                           Helmut Simonis      Visualization Techniques   8
                               Introduction
               Visualization by Annotation
                    Visualization Interface
                              Conclusions


Practical Example Problems

     Test plan generation (BIBD)
     Progressive party problem
     Routing and wavelength assignment
     Optical network design
     Car sequencing
     Costas arrays
     Sports scheduling
     Still to come
         Production scheduling
         Nurse rostering
         Airport stand allocation


                          Helmut Simonis      Visualization Techniques   9
                                 Introduction
                 Visualization by Annotation
                      Visualization Interface
                                Conclusions


Intention



      Realistic, life like problems
      Must address scalability issues
      Often, problem not completely specified
      Issue: Hard to verify by hand
      Complexity still limited, not real problems
      No attempt at integration




                            Helmut Simonis      Visualization Techniques   10
                                Introduction
                Visualization by Annotation
                     Visualization Interface
                               Conclusions


How do we understand behavior?



     Mental model
     Formal analysis
     Debugging
     Tracing
     Life visualization
     Post-mortem analysis




                           Helmut Simonis      Visualization Techniques   11
                                Introduction
                Visualization by Annotation
                     Visualization Interface
                               Conclusions


How do we understand behavior?



     Mental model
     Formal analysis
     Debugging
     Tracing
     Life visualization
     Post-mortem analysis




                           Helmut Simonis      Visualization Techniques   12
                               Introduction
               Visualization by Annotation
                    Visualization Interface
                              Conclusions


Why Visualize?




     Understand what is done
     Understand what is done in which order
     Understand what is not done
     Understand when to give up




                          Helmut Simonis      Visualization Techniques   13
                               Introduction
               Visualization by Annotation
                    Visualization Interface
                              Conclusions


Conceptual Model



     Stable state at defined program points
     Granularity
         Assign value
         Post constraint
     Show stable state after propagation
     Do not show individual propagation steps




                          Helmut Simonis      Visualization Techniques   14
                                 Introduction
                 Visualization by Annotation
                      Visualization Interface
                                Conclusions


Visualizers




     Search tree
     Variables
     Constraints




                            Helmut Simonis      Visualization Techniques   15
                                Introduction
                Visualization by Annotation
                     Visualization Interface
                               Conclusions


Visualization Tool




      Developed in Java
      Show two panes: tree and state
      Navigate along timeline




                           Helmut Simonis      Visualization Techniques   16
                             Introduction
             Visualization by Annotation
                  Visualization Interface
                            Conclusions


Visualization Tool: Car Sequencing




                        Helmut Simonis      Visualization Techniques   17
                               Introduction
               Visualization by Annotation
                    Visualization Interface
                              Conclusions


How many visualizers do we need?


     Develop few primitives
         Cell based view
         Domain vector
     Allow aggregation
         Vector/matrix
         General layout
     Which global constraints require more?
         Task based view for cumulative
         Matching/flow based representation does not scale




                          Helmut Simonis      Visualization Techniques   18
                                Introduction
                Visualization by Annotation
                     Visualization Interface
                               Conclusions


How to Interpret Visualization




      Search tree
          Good/bad choices
          Place of backtracking
      State
          Missing propagation




                           Helmut Simonis      Visualization Techniques   19
                                                                                          Introduction
                                                                          Visualization by Annotation
                                                                               Visualization Interface
                                                                                         Conclusions


Costas Array Search tree (Size 16)

                                                                                                                                                                                        Deep backtracking
                                                                                                                                                                                        Third choice wrong
                                                                                                                                                                                        Last choice wrong
                                 1
                                  1
                                 2                                                                                                                                                      Value selection
                                  2


                             4
                                 3
                                  5     6
                                                                                                                                                                                        strategy useless
                                            4
                    114611     124619
                335881
                             4
                         3 361038 5         7     8      9       10 11
                                                                                            5
     4950     7156       5581                     6966           9250
   14515    21155      16169                    19916        26568
                                                                                        3    4        5
                                                                                                          6
                                                                              627           801
                                                                          1897
                                                                                        4
                                                                                    3 2442        7       8        9    10 12 13
                                                                                                                                                 9
                                                            47           45            61          66                                   66
                                                      150          127           176         200
                                                                                                                               3   4 7
                                                                                                                                   200
                                                                                                                                             8   9   10 12 14 15
                                                                                                                                                                                        7
                                                                                                   24              20         20        4                 17        11         28
                                                                                             77               60         58        15                46        34         98
                                                                                                                                                                                    3   4   7   8
                                                                                                                                                                                                    10
                                                                                                                                                                          6
                                                                                                                                                                     14
                                                                                                                                                                                                    12 14
                                                                                                                                                                                                         12
                                                                                                                                                                                                     3    7   9




                                                                                                                   Helmut Simonis                                    Visualization Techniques                     20
                                                                                          Introduction
                                                                          Visualization by Annotation
                                                                               Visualization Interface
                                                                                         Conclusions


Costas Array Search tree (Size 16)

                                                                                                                                                                                        Deep backtracking
                                                                                                                                                                                        Third choice wrong
                                                                                                                                                                                        Last choice wrong
                                 1
                                  1
                                 2                                                                                                                                                      Value selection
                                  2


                             4
                                 3
                                  5     6
                                                                                                                                                                                        strategy useless
                                            4
                    114611     124619
                335881
                             4
                         3 361038 5         7     8      9       10 11
                                                                                            5
     4950     7156       5581                     6966           9250
   14515    21155      16169                    19916        26568
                                                                                        3    4        5
                                                                                                          6
                                                                              627           801
                                                                          1897
                                                                                        4
                                                                                    3 2442        7       8        9    10 12 13
                                                                                                                                                 9
                                                            47           45            61          66                                   66
                                                      150          127           176         200
                                                                                                                               3   4 7
                                                                                                                                   200
                                                                                                                                             8   9   10 12 14 15
                                                                                                                                                                                        7
                                                                                                   24              20         20        4                 17        11         28
                                                                                             77               60         58        15                46        34         98
                                                                                                                                                                                    3   4   7   8
                                                                                                                                                                                                    10
                                                                                                                                                                          6
                                                                                                                                                                     14
                                                                                                                                                                                                    12 14
                                                                                                                                                                                                         12
                                                                                                                                                                                                     3    7   9




                                                                                                                   Helmut Simonis                                    Visualization Techniques                     21
                                                                                          Introduction
                                                                          Visualization by Annotation
                                                                               Visualization Interface
                                                                                         Conclusions


Costas Array Search tree (Size 16)

                                                                                                                                                                                        Deep backtracking
                                                                                                                                                                                        Third choice wrong
                                                                                                                                                                                        Last choice wrong
                                 1
                                  1
                                 2                                                                                                                                                      Value selection
                                  2


                             4
                                 3
                                  5     6
                                                                                                                                                                                        strategy useless
                                            4
                    114611     124619
                335881
                             4
                         3 361038 5         7     8      9       10 11
                                                                                            5
     4950     7156       5581                     6966           9250
   14515    21155      16169                    19916        26568
                                                                                        3    4        5
                                                                                                          6
                                                                              627           801
                                                                          1897
                                                                                        4
                                                                                    3 2442        7       8        9    10 12 13
                                                                                                                                                 9
                                                            47           45            61          66                                   66
                                                      150          127           176         200
                                                                                                                               3   4 7
                                                                                                                                   200
                                                                                                                                             8   9   10 12 14 15
                                                                                                                                                                                        7
                                                                                                   24              20         20        4                 17        11         28
                                                                                             77               60         58        15                46        34         98
                                                                                                                                                                                    3   4   7   8
                                                                                                                                                                                                    10
                                                                                                                                                                          6
                                                                                                                                                                     14
                                                                                                                                                                                                    12 14
                                                                                                                                                                                                         12
                                                                                                                                                                                                     3    7   9




                                                                                                                   Helmut Simonis                                    Visualization Techniques                     22
                                                                                          Introduction
                                                                          Visualization by Annotation
                                                                               Visualization Interface
                                                                                         Conclusions


Costas Array Search tree (Size 16)

                                                                                                                                                                                        Deep backtracking
                                                                                                                                                                                        Third choice wrong
                                                                                                                                                                                        Last choice wrong
                                 1
                                  1
                                 2                                                                                                                                                      Value selection
                                  2


                             4
                                 3
                                  5     6
                                                                                                                                                                                        strategy useless
                                            4
                    114611     124619
                335881
                             4
                         3 361038 5         7     8      9       10 11
                                                                                            5
     4950     7156       5581                     6966           9250
   14515    21155      16169                    19916        26568
                                                                                        3    4        5
                                                                                                          6
                                                                              627           801
                                                                          1897
                                                                                        4
                                                                                    3 2442        7       8        9    10 12 13
                                                                                                                                                 9
                                                            47           45            61          66                                   66
                                                      150          127           176         200
                                                                                                                               3   4 7
                                                                                                                                   200
                                                                                                                                             8   9   10 12 14 15
                                                                                                                                                                                        7
                                                                                                   24              20         20        4                 17        11         28
                                                                                             77               60         58        15                46        34         98
                                                                                                                                                                                    3   4   7   8
                                                                                                                                                                                                    10
                                                                                                                                                                          6
                                                                                                                                                                     14
                                                                                                                                                                                                    12 14
                                                                                                                                                                                                         12
                                                                                                                                                                                                     3    7   9




                                                                                                                   Helmut Simonis                                    Visualization Techniques                     23
                            Introduction
            Visualization by Annotation
                 Visualization Interface
                           Conclusions


Missing Propagation

                                                          The model is
                                                          doing this




                       Helmut Simonis      Visualization Techniques      24
                            Introduction
            Visualization by Annotation
                 Visualization Interface
                           Conclusions


Missing Propagation

                                                          It could be doing
                                                          that!




                       Helmut Simonis      Visualization Techniques           25
                                                                                                                                        Introduction
                                                                                                                        Visualization by Annotation
                                                                                                                             Visualization Interface
                                                                                                                                       Conclusions


Comparison (Search Tree, size 16)

                                                                   Initial Model                                                                                                                                                                   Improved Model
                                                                                                                                                                                                                                            1
                                                                                                                                                                                                                                               1
                                                                                                                                                                                                                                            2
                                                                                                                                                                                                                                               2
                                 1
                                  1
                                                                                                                                                                                                                                            3
                                 2                                                                                                                                                                                                    4        5       6
                                  2
                                 3                                                                                                                                                                                                                         4
                                                                                                                                                                                                                            55029          61250
                             4    5     6
                                                                                                                                                                                                                          106926
                                                                                                                                                                                                                                           3
                                                                                                                                                                                                                                      119643
                                                                                                                                                                                                                                                   4       5     8         9     11
                                            4
                    114611
                335881
                             4
                               124619
                         3 361038 5         7     8      9       10 11                                                                                                                                                                                                                            5
                                                                                            5                                                                                                                        2729           3284           2980          3668            4011
     4950     7156       5581                     6966           9250
                                                                                        3    4        5                                                                                                            5186       6345             5726            7056            7927
                                                                                                                                                                                                                                                                                            3       4        5
   14515    21155      16169                    19916        26568


                                                                              627
                                                                                    3 2442
                                                                                        4
                                                                                            801
                                                                                                  7
                                                                                                          6
                                                                                                          8        9    10 12 13
                                                                                                                                                                                                                                                                                                                 6
                                                                          1897                                                                                                                                                                                                   351            373
                                                                                                                                                 9                                                                                                                             667          727
                                                                                                                                                                                                                                                                                                3        4       7        8    12 13
                                                            47           45            61          66                                   66
                                                      150          127           176         200
                                                                                                                               3   4 7
                                                                                                                                   200
                                                                                                                                             8   9   10 12 14 15
                                                                                                                                                                                        7
                                                                                                                                                                                                                                                                                                                                               7
                                                                                                                                                                                                                                                                           30              23            24               43         35
                                                                                                                                                                                                                                                                                                                                               3       8
                                                                                                   24              20         20        4                 17        11         28
                                                                                             77               60         58        15                46        34         98
                                                                                                                                                                                    3   4   7   8
                                                                                                                                                                                                                                                                      55              37            43               82         66
                                                                                                                                                                                                    10
                                                                                                                                                                     14
                                                                                                                                                                          6
                                                                                                                                                                                                    12 14                                                                                                                                              8
                                                                                                                                                                                                                                                                                                                                           8
                                                                                                                                                                                                         12                                                                                                                                                4
                                                                                                                                                                                                     3    7   9                                                                                                                       15

                                                                                                                                                                                                                                                                                                                                                       9
                                                                                                                                                                                                                                                                                                                                                   3       14 15
                                                                                                                                                                                                                                                                                                                                                               10
                                                                                                                                                                                                                                                                                                                                           1           3
                                                                                                                                                                                                                                                                                                                                      2            4
                                                                                                                                                                                                                                                                                                                                                               12 14




                                                                                                                                                               Helmut Simonis                                     Visualization Techniques                                                                                                                             26
                             Introduction
             Visualization by Annotation
                  Visualization Interface
                            Conclusions


Progressive Party Problem, 9 Time Periods
                          root
                      -      -       -
                                         1
               2804       1686
             4251     2929                   7
                                         2
                                             11
                                         3
                                             5
                                         4
                                             3
                                         5
                                             2
                                         6
                                             2
                                         7
                                             9
                                         8
                                             1
                                         9
                                             1
                                         10
                                             4
                                         11
                                             6
                                         12
                                             4
                                         13
                                             12
                                         14
                                             8
                                         15
                                 3       6       9   10
                                                          16
                                                              3
                                                          17
                                                              9
                                                          18
                                                              3
                                                          19
                                                              13
                                                          20
                                                              1
                                                          21
                                                              8
                                                          22
                                                              9
                                                          23
                                                              13
                                                          24
                                                              6
                                                          25
                                                              5
                                                          26
                                                              8
                                                          27
                                                              6
                                                          30
                                                              10
                                                          31
                                                              3
                                                          32
                                                              8
                                                          33
                                                              1
                                                          34
                                                              5
                                                          35
                                                              9
                                                          36
                                                              11
                                                          37
                                                              9
                                                          38
                                                              7
                                                          39
                                                              12
                                                          40
                                                              1
                                                          41
                                                              2
                                                          42
                                                              13
                                                          43
                                                              5
                                                          44
                                                              6
                                                          45
                                                              6
                                                          46
                                                              8
                                                          47
                                                              11
                                                          48
                                                              2
                                                          49
                                                              2
                                                          50
                                                              2
                                                          51
                                                              7
                                                          52
                                                              6
                                                          53
                                                              4
                                                          54
                                                          3       4
                                                                  55
                                                                  3    4
                                                                       56
                                                                           3
                                                                       57
                                                                           7
                                                                       59
                                                                           5
                                                                       60
                                                                           9
                                                                       61
                                                                           10
                                                                       62
                                                                           11
                                                                       63
                                                                           4
                                                                       64
                                                                           8
                                                                       65
                                                                           3
                                                                       66
                                                                           7
                                                                       67
                                                                           2
                                                                       68
                                                                           7
                                                                       69
                                                                           12
                                                                       70
                                                                           13
                                                                       71
                                                                           2
                                                                       72
                                                                           6
                                                                       73
                                                                           4
                                                                       74
                                                                           9
                                                                       75
                                                                           1
                                                                       76
                                                                           1
                                                                       77
                                                                           3
                                                                       78
                                                                           10
                                                                       80
                                                                           8
                                                                       81
                                                                           1
                                                                       82
                                                                           8
                                                                       83
                                                                  3    2       1       6
                                                                                           84
                                                                                            3
                                                                                           85
                                                                                            2
                                                                                           88
                                                                                            8
                                                                                           89
                                                                                            5
                                                                                           90
                                                                                            9
                                                                                           91
                                                                                            10
                                                                                           92
                                                                                            7
                                                                                           93
                                                                                            6
                                                                                           94
                                                                                            13
                                                                                           95
                                                                                            2
                                                                                           96
                                                                                            6
                                                                                           97
                                                                                            1
                                                                                           98
                                                                                            3
                                                                                           99
                                                                                            3
                                                                                           100
                                                                                            4
                                                                                           101
                                                                                            9
                                                                                           102
                                                                                            11
                                                                                           103
                                                                                            2
                                                                                           104
                                                                                            7
                                                                                           105
                                                                                            4
                                                                                           106
                                                                                            10
                                                                                           107
                                                                                           11 4
                                                                                                108
                                                                                       1
                                                                                   2
                                                                                                    12
                                                                                                111
                                                                                                    12
                                                                                                117
                                                                                                    9
                                                                                                118
                                                                                                    1
                                                                                                119
                                                                                                    11
                                                                                                120
                                                                                                    4
                                                                                                121
                                                                                                    6
                                                                                                122
                                                                                                    12
                                                                                                123
                                                                                                    2
                                                                                                124
                                                                                                    8
                                                                                                125
                                                                                                    10
                                                                                                126
                                                                                                    2
                                                                                                127
                                                                                                    8
                                                                                                128
                                                                                                    1
                                                                                                129
                                                                                                    3
                                                                                                130
                                                                                                7       4
                                                                                                     132
                                                                                                            7
                                                                                                     133
                                                                                                            3
                                                                                                     134
                                                                                                10 6             13 5
                                                                                                                        135
                                                                                       5         8               7
                                                                                   9        9               11
                                                                                                                        6   5
                                                                                                                            136
                                                                                                                            6     7
                                                                                                                                 137
                                                                                                                                      13
                                                                                                                                 138
                                                                                                                                      13
                                                                                                                                 146
                                                                                                                                      3
                                                                                                                                 147
                                                                                                                                      2
                                                                                                                                 148
                                                                                                                                      4
                                                                                                                                 149
                                                                                                                                      9
                                                                                                                                 150
                                                                                                                                      8
                                                                                                                                 151
                                                                                                                                      7
                                                                                                                                 152
                                                                                                                                      7
                                                                                                                                 153
                                                                                                                                      6
                                                                                                                                 154
                                                                                                                                      13
                                                                                                                                 155
                                                                                                                                      5
                                                                                                                                 156
                                                                                                                                      5
                                                                                                                                 157
                                                                                                                                      6
                                                                                                                                 158
                                                                                                                                      1
                                                                                                                                 159
                                                                                                                                      10
                                                                                                                                 160
                                                                                                                                      9
                                                                                                                                 161
                                                                                                                                      1
                                                                                                                                 162
                                                                                                                                      10
                                                                                                                                 163
                                                                                                                                      2
                                                                                                                                 164
                                                                                                                                      4
                                                                                                                                 165
                                                                                                                                      12
                                                                                                                                 166
                                                                                                                                  11 3
                                                                                                                                        167
                                                                                                                                          12 11
                                                                                                                                            175
                                                                                                                                                 6
                                                                                                                                            176
                                                                                                                                                 7
                                                                                                                                            177
                                                                                                                                                 1
                                                                                                                                            178
                                                                                                                                                 8
                                                                                                                                            179
                                                                                                                                                 3
                                                                                                                                            180
                                                                                                                                           10 5      1
                                                                                                                                                         181
                                                                                                                                  277         210
                                                                                                                                387        298             4
                                                                                                                                                         182
                                                                                                                                                           11
                                                                                                                                                         183
                                                                                                                                                           9
                                                                                                                                                         184
                                                                                                                                                           9
                                                                                                                                                         185
                                                                                                                                                          13 2
                                                                                                                                                               186
                                                                                                                                                     2
                                                                                                                                                 4              12 5
                                                                                                                                                                     187
                                                                                                                                                          8
                                                                                                                                                     10
                                                                                                                                                                       10
                                                                                                                                                                     190
                                                                                                                                                                       13
                                                                                                                                                                     191
                                                                                                                                                                       5
                                                                                                                                                                     193
                                                                                                                                                                       11
                                                                                                                                                                     194
                                                                                                                                                                       8
                                                                                                                                                                     204
                                                                                                                                                                       1
                                                                                                                                                                     205
                                                                                                                                                                       10
                                                                                                                                                                     206
                                                                                                                                                                       3
                                                                                                                                                                     207
                                                                                                                                                                       2
                                                                                                                                                                     208
                                                                                                                                                                       9
                                                                                                                                                                     209
                                                                                                                                                                       5
                                                                                                                                                                     210
                                                                                                                                                                       12
                                                                                                                                                                     211
                                                                                                                                                                       3
                                                                                                                                                                     212
                                                                                                                                                                       8
                                                                                                                                                                     213
                                                                                                                                                                     11 6
                                                                                                                                                                        214
                                                                                                                                                                29
                                                                                                                                                           60               4
                                                                                                                                                                        215
                                                                                                                                                                            7
                                                                                                                                                                        216
                                                                                                                                                                            7
                                                                                                                                                                        217
                                                                                                                                                                       13 1     11
                                                                                                                                                                                    219
                                                                                                                                                                2           6
                                                                                                                                                           7           13           8    11
                                                                                                                                                                                         220
                                                                                                                                                                                1
                                                                                                                                                                            2       4    13 6   2
                                                                                                                                                                                                    221
                                                                                                                                                                                     1
                                                                                                                                                                                3
                                                                                                                                                                                                6   9   8   13
                                                                                                                                                                                                                 222
                                                                                                                                                                                                             6    9    8
                                                                                                                                                                                                                           224
                                                                                                                                                                                                                           5        9
                                                                                                                                                                                                                                233
                                                                                                                                                                                                                                    4        2
                                                                                                                                                                                                                                         234
                                                                                                                                                                                                                            2
                                                                                                                                                                                                                       3
                                                                                                                                                                                                                                                 4
                                                                                                                                                                                                                                         235
                                                                                                                                                                                                                                             6       7
                                                                                                                                                                                                                                                     236
                                                                                                                                                                                                                                    34
                                                                                                                                                                                                                               64                        5
                                                                                                                                                                                                                                                     237
                                                                                                                                                                                                                                                         1
                                                                                                                                                                                                                                                     238
                                                                                                                                                                                                                                                     11 3
                                                                                                                                                                                                                                                          239
                                                                                                                                                                                                                                             19
                                                                                                                                                                                                                                        25
                                                                                                                                                                                                                                                                 6
                                                                                                                                                                                                                                                          240
                                                                                                                                                                                                                                                                 10
                                                                                                                                                                                                                                                          241
                                                                                                                                                                                                                                                                 11
                                                                                                                                                                                                                                                          242
                                                                                                                                                                                                                                                             8       13
                                                                                                                                                                                                                                                                 244
                                                                                                                                                                                                                                                      2
                                                                                                                                                                                                                                                 3                   12 8
                                                                                                                                                                                                                                                                          248
                                                                                                                                                                                                                                                                          8    12
                                                                                                                                                                                                                                                                              249
                                                                                                                                                                                                                                                                              12 11 4
                                                                                                                                                                                                                                                                                    250
                                                                                                                                                                                                                                                                                        9   10




                                                                                                                                                                                                                                                                                                 Helmut Simonis   Visualization Techniques   27
                                    Introduction
                    Visualization by Annotation
                         Visualization Interface
                                   Conclusions


2 Restarts Before Solution Found

                         root
                     -      -   -
                                    1
             2804        1686
           4251      2929
                                     7
                                    2
                                     11
                                    3
                                     5
                                    4
                                     3
                                    5
                                     2
                                    6
                                     2
                                    7
                                     9
                                    8
                                     1
                                    9
                                     1
                                    10
                                     4
                                     Helmut Simonis   Visualization Techniques   28
                  208
                   9                                             Introduction
                  209
                   5                             Visualization by Annotation
                  210
                   12                                 Visualization Interface
                  211
                   3                                            Conclusions
                  212
                   8


Value Choice Strategy Not Focused
             29
                  213
                  11 6
                    214
                         4
        60

                    215
                         7
                    216
                         7
                    217
                   13 1      11
                                 219
             2          6
        7          13
                                 8    11
                                      220
                             1
                         2
                                 4    13 6   2
                                                 221
                                  1
                             3
                                             6   9   8   13
                                                              222
                                                          6    9    8
                                                                        224
                                                                        5        9
                                                                             233
                                                                                 4        2
                                                                                      234
                                                                         2
                                                                    3
                                                                                              4
                                                                                      235
                                                                                          6       7
                                                                                                  236
                                                                                 34
                                                                            64
                                                                                                      5
                                                                                                  237
                                                                                                      1
                                                                                                  238
                                                                                                  11 3
                                                                                                       239
                                                                                          19
                                                                                     25
                                                                                                              6
                                                                                                       240
                                                                                                              10
                                                                                                       241
                                                                                                              11
                                                                                                       242
                                                                                                          8       13
                                                                                                              244
                                                                                                   2
                                                                                              3
                                                                                                                  12 8
                                                                                                                       248
                                                                                                                       8    12
                                                                                                                           249
                                                                                                                           12 11 4
                                                                                                                                 250
                                                                                                                                     9   10




                                                                                      Helmut Simonis                                          Visualization Techniques   29
                               Introduction
               Visualization by Annotation
                    Visualization Interface
                              Conclusions


Progressive Party




     Clearly impossible to explore search space
     Either many solutions or good value selection
     Value selection at end rather poor
     Probably many solutions




                          Helmut Simonis      Visualization Techniques   30
                                                                                   Introduction
                                                                   Visualization by Annotation
                                                                        Visualization Interface
                                                                                  Conclusions


Missing Propagation: Shikaku

             9        9        29 13     29                   29         29                   33
     1           1        1     9 1           16   29              22         25    29             29
         4                                                                                6
    9        9                 16 13                          29 22      29         33 30
         1       1     9        9        16 16                16              25    29        33
                           6                   3                                                    2
    13 9     13 10    13 10              22 16     25 22      25 22                 30        33 30
     1        9        9       13        13        13         13         25              25   25
                                     4                                         3
    10                         14 13     22 16     30 22      30         30 26
         1   10 10             10        13 10     19 10           22    25         30 30
                           4                                                              4
                               14        22        22 19                 30 26      30        34
     2        2        2            13        17   17         22         25              26        30
                                                                    9
                               14        26 22     26 22      26                    31 30     34
     2        2        2            13   17 14     19 17           22    26         26             26
                                                                               4
                                         22 17     22 19      26 23 22   26         31 30
     2        2        2       14        14        17 14
                                                              19 17 14
                                                                              17    26        34
         9                           4
                                                   19         23 22      31 26                34
     3        5        5        5        17             17    19 17      19 17      31             31
                  6                            8
                                                              31 23      31 26                34
     3        5        5        5        18 19                22 19      19         31             31
         6                                               6                                4
                                                   20         23 22      32 31 27   32
     3        6        6        6        18             19    20 19
                                                                         23 19
                                                                                         31   34
                  9                            4                                                    6
                                                              32 23      32 27                35 34
     3        6        6        6        18 20                22 20      23         32        32
                                                         4                                4
                                                   23                    32 27      35 32
     3        6        6        6        18             20    23         23         23        35
                                                                    6                               2
                               15        15        23 20      27 24      27         32 27     36
     3       11 11                  11        11   15 11      23 15           23    23             35
                           4
    15 7     15 11    15 11                        27 23      27 24      27 23      32 27     36 27
     4        7        7       15 15               20 15      23 15      15         15        15
                                     8
    7                 27 15    27 15     27 15     27 24 21   27 24 23                        36
         4    7       12 7      7         7
                                                   15 7       15 7
                                                                         27 27                     27
                  6                                                            6
    7        12 7              24 15     24        24                    28 27      36 28     36 28
         4    4       12       12             15        21    24         24         27 24     27 24
                           2                                        4
             8        12 8     21 15     21                   28 24                 36        36
     4           4     4        4             15   21         21         28              28        28
         4                                               3                     6
    8                                    36        36         36 28      36         36
         4    8        8        8             8         21    24              28         28   36
                  4                                                                                 6




                                                                                                   Helmut Simonis   Visualization Techniques   31
                                     Introduction
                     Visualization by Annotation
                          Visualization Interface
                                    Conclusions


Outline


  1   Introduction

  2   Visualization by Annotation

  3   Visualization Interface

  4   Conclusions




                                Helmut Simonis      Visualization Techniques   32
                             Introduction
             Visualization by Annotation
                  Visualization Interface
                            Conclusions


Sendmore Program Annotated

  sendmory(L,Output,IgnoreFixed):-
    L=[S,E,N,D,M,O,R,Y],
    L :: 0..9,
    create_visualization([output:Output,
                          ignore_fixed:IgnoreFixed,
                          width:8,
                          height:10],Handle),
    add_visualizer(Handle,
                   vector(L),
                   [display:expanded]),
    alldifferent(L),draw_visualization(Handle),
    S #\= 0,draw_visualization(Handle),
    M #\= 0,draw_visualization(Handle),

                        Helmut Simonis      Visualization Techniques   33
                             Introduction
             Visualization by Annotation
                  Visualization Interface
                            Conclusions


Sendmore Program Annotated

  sendmory(L,Output,IgnoreFixed):-
    L=[S,E,N,D,M,O,R,Y],
    L :: 0..9,
    create_visualization([output:Output,
                          ignore_fixed:IgnoreFixed,
                          width:8,
                          height:10],Handle),
    add_visualizer(Handle,
                   vector(L),
                   [display:expanded]),
    alldifferent(L),draw_visualization(Handle),
    S #\= 0,draw_visualization(Handle),
    M #\= 0,draw_visualization(Handle),

                        Helmut Simonis      Visualization Techniques   34
                             Introduction
             Visualization by Annotation
                  Visualization Interface
                            Conclusions


Sendmore Program Annotated

  sendmory(L,Output,IgnoreFixed):-
    L=[S,E,N,D,M,O,R,Y],
    L :: 0..9,
    create_visualization([output:Output,
                          ignore_fixed:IgnoreFixed,
                          width:8,
                          height:10],Handle),
    add_visualizer(Handle,
                   vector(L),
                   [display:expanded]),
    alldifferent(L),draw_visualization(Handle),
    S #\= 0,draw_visualization(Handle),
    M #\= 0,draw_visualization(Handle),

                        Helmut Simonis      Visualization Techniques   35
                             Introduction
             Visualization by Annotation
                  Visualization Interface
                            Conclusions


Sendmore Program Annotated

  sendmory(L,Output,IgnoreFixed):-
    L=[S,E,N,D,M,O,R,Y],
    L :: 0..9,
    create_visualization([output:Output,
                          ignore_fixed:IgnoreFixed,
                          width:8,
                          height:10],Handle),
    add_visualizer(Handle,
                   vector(L),
                   [display:expanded]),
    alldifferent(L),draw_visualization(Handle),
    S #\= 0,draw_visualization(Handle),
    M #\= 0,draw_visualization(Handle),

                        Helmut Simonis      Visualization Techniques   36
                             Introduction
             Visualization by Annotation
                  Visualization Interface
                            Conclusions


Sendmore Program Annotated

  sendmory(L,Output,IgnoreFixed):-
    L=[S,E,N,D,M,O,R,Y],
    L :: 0..9,
    create_visualization([output:Output,
                          ignore_fixed:IgnoreFixed,
                          width:8,
                          height:10],Handle),
    add_visualizer(Handle,
                   vector(L),
                   [display:expanded]),
    alldifferent(L),draw_visualization(Handle),
    S #\= 0,draw_visualization(Handle),
    M #\= 0,draw_visualization(Handle),

                        Helmut Simonis      Visualization Techniques   37
                             Introduction
             Visualization by Annotation
                  Visualization Interface
                            Conclusions


Sendmore Program Annotated

  sendmory(L,Output,IgnoreFixed):-
    L=[S,E,N,D,M,O,R,Y],
    L :: 0..9,
    create_visualization([output:Output,
                          ignore_fixed:IgnoreFixed,
                          width:8,
                          height:10],Handle),
    add_visualizer(Handle,
                   vector(L),
                   [display:expanded]),
    alldifferent(L),draw_visualization(Handle),
    S #\= 0,draw_visualization(Handle),
    M #\= 0,draw_visualization(Handle),

                        Helmut Simonis      Visualization Techniques   38
                            Introduction
            Visualization by Annotation
                 Visualization Interface
                           Conclusions


Sendmore Program Annotated

   1000*S + 100*E + 10*N + D +
   1000*M + 100*O + 10*R + E #=
   10000*M + 1000*O + 100*N + 10*E + Y,
   name_variables(Handle,L,
                  [’S’,’E’,’N’,’D’,’M’,’O’,’R’,’Y’],
                  Pairs),
   root(Handle),
   search(Pairs,1,input_order,
          tree_indomain(Handle,_),
          complete,[]),
   solution(Handle),
   close_visualization(Handle).

                       Helmut Simonis      Visualization Techniques   39
                            Introduction
            Visualization by Annotation
                 Visualization Interface
                           Conclusions


Sendmore Program Annotated

   1000*S + 100*E + 10*N + D +
   1000*M + 100*O + 10*R + E #=
   10000*M + 1000*O + 100*N + 10*E + Y,
   name_variables(Handle,L,
                  [’S’,’E’,’N’,’D’,’M’,’O’,’R’,’Y’],
                  Pairs),
   root(Handle),
   search(Pairs,1,input_order,
          tree_indomain(Handle,_),
          complete,[]),
   solution(Handle),
   close_visualization(Handle).

                       Helmut Simonis      Visualization Techniques   40
                            Introduction
            Visualization by Annotation
                 Visualization Interface
                           Conclusions


Sendmore Program Annotated

   1000*S + 100*E + 10*N + D +
   1000*M + 100*O + 10*R + E #=
   10000*M + 1000*O + 100*N + 10*E + Y,
   name_variables(Handle,L,
                  [’S’,’E’,’N’,’D’,’M’,’O’,’R’,’Y’],
                  Pairs),
   root(Handle),
   search(Pairs,1,input_order,
          tree_indomain(Handle,_),
          complete,[]),
   solution(Handle),
   close_visualization(Handle).

                       Helmut Simonis      Visualization Techniques   41
                            Introduction
            Visualization by Annotation
                 Visualization Interface
                           Conclusions


Sendmore Program Annotated

   1000*S + 100*E + 10*N + D +
   1000*M + 100*O + 10*R + E #=
   10000*M + 1000*O + 100*N + 10*E + Y,
   name_variables(Handle,L,
                  [’S’,’E’,’N’,’D’,’M’,’O’,’R’,’Y’],
                  Pairs),
   root(Handle),
   search(Pairs,1,input_order,
          tree_indomain(Handle,_),
          complete,[]),
   solution(Handle),
   close_visualization(Handle).

                       Helmut Simonis      Visualization Techniques   42
                            Introduction
            Visualization by Annotation
                 Visualization Interface
                           Conclusions


Sendmore Program Annotated

   1000*S + 100*E + 10*N + D +
   1000*M + 100*O + 10*R + E #=
   10000*M + 1000*O + 100*N + 10*E + Y,
   name_variables(Handle,L,
                  [’S’,’E’,’N’,’D’,’M’,’O’,’R’,’Y’],
                  Pairs),
   root(Handle),
   search(Pairs,1,input_order,
          tree_indomain(Handle,_),
          complete,[]),
   solution(Handle),
   close_visualization(Handle).

                       Helmut Simonis      Visualization Techniques   43
                            Introduction
            Visualization by Annotation
                 Visualization Interface
                           Conclusions


Sendmore Program Annotated

   1000*S + 100*E + 10*N + D +
   1000*M + 100*O + 10*R + E #=
   10000*M + 1000*O + 100*N + 10*E + Y,
   name_variables(Handle,L,
                  [’S’,’E’,’N’,’D’,’M’,’O’,’R’,’Y’],
                  Pairs),
   root(Handle),
   search(Pairs,1,input_order,
          tree_indomain(Handle,_),
          complete,[]),
   solution(Handle),
   close_visualization(Handle).

                       Helmut Simonis      Visualization Techniques   44
                            Introduction
            Visualization by Annotation
                 Visualization Interface
                           Conclusions


Sendmore Program Annotated

   1000*S + 100*E + 10*N + D +
   1000*M + 100*O + 10*R + E #=
   10000*M + 1000*O + 100*N + 10*E + Y,
   name_variables(Handle,L,
                  [’S’,’E’,’N’,’D’,’M’,’O’,’R’,’Y’],
                  Pairs),
   root(Handle),
   search(Pairs,1,input_order,
          tree_indomain(Handle,_),
          complete,[]),
   solution(Handle),
   close_visualization(Handle).

                       Helmut Simonis      Visualization Techniques   45
                              Introduction
              Visualization by Annotation
                   Visualization Interface
                             Conclusions


Sudoku Program Annotated
  model(Matrix,Method,Output):-
    Matrix[1..9,1..9] :: 1..9,
    create_visualization([output:Output,
                          width:9,
                          height:9],Handle),
    add_visualizer(Handle,
                   domain_matrix(Matrix),
                   [display:text]),
    draw_visualization(Handle),
    (for(I,1,9),
     param(Matrix,Method,Handle) do
        Method:alldifferent(Matrix[I,1..9]),
        draw_visualization(Handle,[focus:row(I)]),
        Method:alldifferent(Matrix[1..9,I]),
        draw_visualization(Handle,[focus:col(I)])
    ),
                         Helmut Simonis      Visualization Techniques   46
                             Introduction
             Visualization by Annotation
                  Visualization Interface
                            Conclusions


Sudoku Program Annotated

   (multifor([I,J],[1,1],[7,7],[3,3]),
    param(Matrix,Method,Handle) do
       Method:alldifferent(Matrix[I..I+2,J..J+2]),
       draw_visualization(Handle,
                          [focus:block(I,J,3,3)])
   ),
   extract_array(Handle,row,Matrix,NamedList),
   root(Handle),
   search(NamedList,1,input_order,
          tree_indomain(Handle,_),
          complete,[]),
   solution(Handle),
   close_visualization(Handle).


                        Helmut Simonis      Visualization Techniques   47
                                                           Introduction
                                           Visualization by Annotation
                                                Visualization Interface
                                                          Conclusions


Propagation Steps (Forward Checking)
               1   2   3               1 2 3 1 2 3 1   2   3   1   2   3   1   2   3   1   2   3

      4        4
               7
                   5
                   8
                       6
                       9       8       4 5 6 4 5 6 4
                                       7 8 9 7 8 9 7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2    3   1   2   3   1   2   3               1   2   3   1   2   3   1   2   3   1   2   3
  4
  7
      5
      8
           6
           9
               4
               7
                   5
                   8
                       6
                       9
                           4
                           7
                               5
                               8
                                   6
                                   9    1 7        4
                                                   7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2    3   1   2   3   1   2   3   1 2 3       1   2   3   1   2   3
  4
  7
      5
      8
           6
           9
               4
               7
                   5
                   8
                       6
                       9
                           4
                           7
                               5
                               8
                                   6
                                   9      8
                                       4 5 6
                                       7 8 9
                                                   4
                                                   7
                                                       5
                                                       8   3 2
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
  1   2    3   1   2   3               1 2 3 1 2 3                                     1   2   3
  4
  7
      5
      8
           6
           9
               4
               7
                   5
                   8
                       6
                       9       6       4 5 6 4 5 6
                                       7 8 9 7 8 9     8 2 5                           4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2    3               1 2 3       1 2 3 1 2 3 1   2   3   1 2 3                   1   2   3
  4
  7
      5
      8 9  6
           9
                           4 5 6
                           7 8 9
                                       4 5 6 4 5 6 4
                                       7 8 9 7 8 9 7
                                                       5
                                                       8   8
                                                           6
                                                           9
                                                               4 5 6
                                                               7 8 9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2    3                                 1 2 3 1   2   3               1   2   3   1   2   3
  4
  7
      5
      8 3 7 6
           6
           9
                                             4 5 6 4
                                             7 8 9 7
                                                       5
                                                       8 9 6
                                                           9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
                           1   2   3   1 2 3       1   2   3   1   2   3   1   2   3   1   2   3

      2 7     5            4
                           7
                               5
                               8
                                   6
                                   9
                                       4 5 6
                                       7 8 9
                                                   4
                                                   7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2    3   1   2   3   1   2   3   1 2 3                   1   2   3   1   2   3   1   2   3
  4
  7
      5
      8
           6
           9  1 4
               4
               7
                   5
                   8
                       6
                       9
                           4
                           7
                               5
                               8
                                   6
                                   9
                                       4 5 6
                                       7 8 9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2    3   1   2   3   1   2   3   1 2 3 1 2 3 1   2 3                 1   2   3
  4
  7
      5
      8
           6
           9
               4
               7
                   5
                   8
                       6
                       9
                           4
                           7
                               5
                               8
                                   6
                                   9
                                       4 5 6 4 5 6 4
                                       7 8 9 7 8 9 7
                                                       5 6
                                                       8 9         6       4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9       4
          Skip Animation


                                                       Helmut Simonis                      Visualization Techniques   48
                                                          Introduction
                                          Visualization by Annotation
                                               Visualization Interface
                                                         Conclusions


Propagation Steps (Forward Checking)
              1   2   3               1 2 3 1 2 3 1    2   3   1   2   3   1   2   3   1   2   3

      4       4
              7
                  5
                  8
                      6
                      9       8       4 5 6 4 5 6 4
                                      7 8 9 7 8 9 7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3   1   2   3   1   2   3               1    2   3   1   2   3   1   2   3   1   2   3
  4
  7
      5
      8
          6
          9
              4
              7
                  5
                  8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9    1 7        4
                                                  7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3   1   2   3   1   2   3   1 2 3       1    2   3   1   2   3
  4
  7
      5
      8
          6
          9
              4
              7
                  5
                  8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9      8
                                      4 5 6
                                      7 8 9
                                                  4
                                                  7
                                                       5
                                                       8  3 2
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
  1   2   3   1   2   3               1 2 3 1 2 3                                      1   2   3
  4
  7
      5
      8
          6
          9
              4
              7
                  5
                  8
                      6
                      9       6       4 5 6 4 5 6
                                      7 8 9 7 8 9     8 2 5                            4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3               1 2 3       1 2 3 1 2 3 1    2   3   1 2 3                   1   2   3
  4
  7
      5
      8 9 6
          9
                          4 5 6
                          7 8 9
                                      4 5 6 4 5 6 4
                                      7 8 9 7 8 9 7
                                                       5
                                                       8  86
                                                           9
                                                               4 5 6
                                                               7 8 9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3                                 1 2 3 1    2   3               1   2   3   1   2   3
  4
  7
      5
      8 3 7 6
          6
          9
                                            4 5 6 4
                                            7 8 9 7
                                                       5
                                                       89  6
                                                           9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
                          1   2   3   1 2 3       1    2   3   1   2   3   1   2   3   1   2   3

      2 7     5           4
                          7
                              5
                              8
                                  6
                                  9
                                      4 5 6
                                      7 8 9
                                                  4
                                                  7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3   1   2   3   1   2   3   1 2 3                    1   2   3   1   2   3   1   2   3
  4
  7
      5
      8
          6
          9   1 4
              4
              7
                  5
                  8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9
                                      4 5 6
                                      7 8 9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3   1   2   3   1   2   3   1 2 3 1 2 3 1    2 3                 1   2   3
  4
  7
      5
      8
          6
          9
              4
              7
                  5
                  8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9
                                      4 5 6 4 5 6 4
                                      7 8 9 7 8 9 7
                                                       5 6
                                                       8 9         6       4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9       4
      Back to Start                   Skip Animation


                                                       Helmut Simonis                      Visualization Techniques   49
                                                          Introduction
                                          Visualization by Annotation
                                               Visualization Interface
                                                         Conclusions


Propagation Steps (Forward Checking)
              1 2     3               1 2 3 1 2 3 1    2 3     1 2     3   1 2     3   1 2     3

      4       7
                5     6
                      9       8       7
                                        5 6
                                          9 7
                                              5 6
                                                9 7
                                                       5 6
                                                         9     7
                                                                 5     6
                                                                       9   7
                                                                             5     6
                                                                                   9   7
                                                                                         5     6
                                                                                               9
  1   2   3   1 2     3   1   2   3               1    2 3     1 2     3   1 2     3   1 2     3
  4
  7
      5
      8
          6
          9
              4 5
              7 8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9    1 7        4
                                                  7
                                                       5 6
                                                       8 9
                                                               4 5
                                                               7 8
                                                                       6
                                                                       9
                                                                           4 5
                                                                           7 8
                                                                                   6
                                                                                   9
                                                                                       4 5
                                                                                       7 8
                                                                                               6
                                                                                               9
  1   2   3   1 2     3   1   2   3   1 2 3       1    2 3     1 2     3
  4
  7
      5
      8
          6
          9
              4 5
              7 8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9      8
                                      4 5 6
                                      7 8 9
                                                  4
                                                  7
                                                       5 6
                                                       8 93 2  4 5
                                                               7 8
                                                                       6
                                                                       9
  1   2   3   1 2     3               1 2 3 1 2 3                                      1   2   3
  4
  7
      5
      8
          6
          9
              4 5
              7 8
                      6
                      9       6       4 5 6 4 5 6
                                      7 8 9 7 8 9     8 2 5                            4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3               1 2 3       1 2 3 1 2 3 1    2   3   1 2 3                   1   2   3
  4
  7
      5
      8 9 6
          9
                          4 5 6
                          7 8 9
                                      4 5 6 4 5 6 4
                                      7 8 9 7 8 9 7
                                                       5
                                                       8  86
                                                           9
                                                               4 5 6
                                                               7 8 9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3                                 1 2 3 1    2   3               1   2   3   1   2   3
  4
  7
      5
      8 3 7 6
          6
          9
                                            4 5 6 4
                                            7 8 9 7
                                                       5
                                                       89  6
                                                           9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
                          1   2   3   1 2 3       1    2   3   1   2   3   1   2   3   1   2   3

      2 7     5           4
                          7
                              5
                              8
                                  6
                                  9
                                      4 5 6
                                      7 8 9
                                                  4
                                                  7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3   1   2   3   1   2   3   1 2 3                    1   2   3   1   2   3   1   2   3
  4
  7
      5
      8
          6
          9   1 4
              4
              7
                  5
                  8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9
                                      4 5 6
                                      7 8 9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3   1   2   3   1   2   3   1 2 3 1 2 3 1    2 3                 1   2   3
  4
  7
      5
      8
          6
          9
              4
              7
                  5
                  8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9
                                      4 5 6 4 5 6 4
                                      7 8 9 7 8 9 7
                                                       5 6
                                                       8 9         6       4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9       4
      Back to Start                   Skip Animation


                                                       Helmut Simonis                      Visualization Techniques   50
                                                      Introduction
                                      Visualization by Annotation
                                           Visualization Interface
                                                     Conclusions


Propagation Steps (Forward Checking)
          1 2     3               1 2 3 1 2 3 1    2 3     1 2     3   1 2     3   1 2     3

      4   7
            5     6
                  9       8       7
                                    5 6
                                      9 7
                                          5 6
                                            9 7
                                                   5 6
                                                     9     7
                                                             5     6
                                                                   9   7
                                                                         5     6
                                                                               9   7
                                                                                     5     6
                                                                                           9
  1   3   1 2     3   1   2   3               1    2 3     1 2     3   1 2     3   1 2     3
    5 6
  7 8 9
          4 5
          7 8
                  6
                  9
                      4
                      7
                          5
                          8
                              6
                              9    1 7        4
                                              7
                                                   5 6
                                                   8 9
                                                           4 5
                                                           7 8
                                                                   6
                                                                   9
                                                                       4 5
                                                                       7 8
                                                                               6
                                                                               9
                                                                                   4 5
                                                                                   7 8
                                                                                           6
                                                                                           9
  1   3   1 2     3   1   2   3   1 2 3       1    2 3     1 2     3
    5 6
  7 8 9
          4 5
          7 8
                  6
                  9
                      4
                      7
                          5
                          8
                              6
                              9      8
                                  4 5 6
                                  7 8 9
                                              4
                                              7
                                                   5 6
                                                   8 93 2  4 5
                                                           7 8
                                                                   6
                                                                   9
  1   3   1 2     3               1 2 3 1 2 3                                      1   2   3
    5 6
  7 8 9
          4 5
          7 8
                  6
                  9       6       4 5 6 4 5 6
                                  7 8 9 7 8 9     8 2 5                            4
                                                                                   7
                                                                                       5
                                                                                       8
                                                                                           6
                                                                                           9
  1   3               1 2 3       1 2 3 1 2 3 1    2   3   1 2 3                   1   2   3
    5 6
  7 8 9 9             4 5 6
                      7 8 9
                                  4 5 6 4 5 6 4
                                  7 8 9 7 8 9 7
                                                   5
                                                   8  86
                                                       9
                                                           4 5 6
                                                           7 8 9
                                                                                   4
                                                                                   7
                                                                                       5
                                                                                       8
                                                                                           6
                                                                                           9
  1   3                                 1 2 3 1    2   3               1   2   3   1   2   3
    5 6
  7 8 9 3 7 6                           4 5 6 4
                                        7 8 9 7
                                                   5
                                                   89  6
                                                       9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
                                                                                   4
                                                                                   7
                                                                                       5
                                                                                       8
                                                                                           6
                                                                                           9
                      1   2   3   1 2 3       1    2   3   1   2   3   1   2   3   1   2   3

      2 7     5       4
                      7
                          5
                          8
                              6
                              9
                                  4 5 6
                                  7 8 9
                                              4
                                              7
                                                   5
                                                   8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
                                                                                   4
                                                                                   7
                                                                                       5
                                                                                       8
                                                                                           6
                                                                                           9
  1   3   1   2   3   1   2   3   1 2 3                    1   2   3   1   2   3   1   2   3
    5 6
  7 8 9
          4
          7   1 4
              5
              8
                  6
                  9
                      4
                      7
                          5
                          8
                              6
                              9
                                  4 5 6
                                  7 8 9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
                                                                                   4
                                                                                   7
                                                                                       5
                                                                                       8
                                                                                           6
                                                                                           9
  1   3   1   2   3   1   2   3   1 2 3 1 2 3 1    2 3                 1   2   3
    5 6
  7 8 9
          4
          7
              5
              8
                  6
                  9
                      4
                      7
                          5
                          8
                              6
                              9
                                  4 5 6 4 5 6 4
                                  7 8 9 7 8 9 7
                                                   5 6
                                                   8 9         6       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9       4
      Back to Start               Skip Animation


                                                   Helmut Simonis                      Visualization Techniques   51
                                                        Introduction
                                        Visualization by Annotation
                                             Visualization Interface
                                                       Conclusions


Propagation Steps (Forward Checking)
            1 2     3               1 2 3 1 2 3 1 2 3 1    2 3 1 2 3 1 2   3

      4     7
              5     6
                    9       8       7
                                      5 6
                                        9 7
                                            5 6
                                              9 7
                                                  5 6
                                                    9 7
                                                           5 6
                                                             9 7
                                                                 5 6
                                                                   9 7
                                                                       5   6
                                                                           9
        3     2     3     2     3                 2 3      2 3   2 3   2   3
      5 6
      8 9
            4 5
              8
                    6
                    9
                        4 5
                          8
                                6
                                9    1 7        4 5 6 4
                                                  8 9
                                                           5 6 4 5 6 4 5
                                                           8 9   8 9   8
                                                                           6
                                                                           9
  1     3   1 2     3   1 2     3   1 2 3       1 2 3 1    2 3

  7
      5 6
      8 9
            4 5
            7 8
                    6
                    9
                        4 5
                        7 8
                                6
                                9      8
                                    4 5 6
                                    7 8 9             3 2
                                                4 5 6 4
                                                7 8 9 7
                                                           5 6
                                                           8 9
  1     3   1 2     3               1 2 3 1 2 3                      1 2   3

  7
      5 6
      8 9
            4 5
            7 8
                    6
                    9       6       4 5 6 4 5 6
                                    7 8 9 7 8 9   8 2 5              4 5
                                                                     7 8
                                                                           6
                                                                           9
  1     3               1 2 3       1 2 3 1 2 3 1 2 3 1    2 3       1 2   3

  7     9
      5 6
      8 9
                        4 5 6
                        7 8 9                         8
                                    4 5 6 4 5 6 4 5 6 4
                                    7 8 9 7 8 9 7 8 9 7
                                                           5 6
                                                           8 9
                                                                     4 5
                                                                     7 8
                                                                           6
                                                                           9
  1     3                                 1 2 3 1 2 3          1 2 3 1 2   3

  7     3 7 6
      5 6
      8 9                                           9
                                          4 5 6 4 5 6
                                          7 8 9 7 8 9
                                                               4 5 6 4 5
                                                               7 8 9 7 8
                                                                           6
                                                                           9
                        1   2   3   1 2 3       1 2 3 1    2 3 1 2 3 1 2   3

      2 7     5         4
                        7
                            5
                            8
                                6
                                9
                                    4 5 6
                                    7 8 9
                                                4 5 6 4
                                                7 8 9 7
                                                           5 6 4 5 6 4 5
                                                           8 9 7 8 9 7 8
                                                                           6
                                                                           9
  1   3     1   2   3   1   2   3   1 2 3             1    2 3 1 2 3 1 2   3
    5 6
  7 8 9
            4
            7 1 4
                5
                8
                    6
                    9
                        4
                        7
                            5
                            8
                                6
                                9
                                    4 5 6
                                    7 8 9
                                                      4
                                                      7
                                                           5 6 4 5 6 4 5
                                                           8 9 7 8 9 7 8
                                                                           6
                                                                           9
  1   3     1   2   3   1   2   3   1 2 3 1 2 3 1 2 3          1 2 3
    5 6
  7 8 9
            4
            7
                5
                8
                    6
                    9
                        4
                        7
                            5
                            8
                                6
                                9
                                    4 5 6 4 5 6 4 5 6
                                    7 8 9 7 8 9 7 8 9     6    4 5 6
                                                               7 8 9   4
      Back to Start                 Skip Animation


                                                     Helmut Simonis    Visualization Techniques   52
                                                  Introduction
                                  Visualization by Annotation
                                       Visualization Interface
                                                 Conclusions


Propagation Steps (Forward Checking)
            1 2               1 2 3 1 2 3 1 2 3 1    2 3 1 2 3 1 2   3

      4       5 6
                    8         7
                                5 6
                                  9 7
                                      5 6
                                        9 7
                                            5 6
                                              9 7
                                                     5 6
                                                       9 7
                                                           5 6
                                                             9 7
                                                                 5   6
                                                                     9
        3     2     2 3                     2 3      2 3   2 3   2   3
      5 6
      8 9
            4 5 6 4 5 6
              8     8 9        1 7        4 5 6 4
                                            8 9
                                                     5 6 4 5 6 4 5
                                                     8 9   8 9   8
                                                                     6
                                                                     9
  1     3   1 2   1 2 3       1 2 3       1 2 3 1    2 3

  7
      5 6
      8 9
            4 5 6 4 5 6
              8   7 8 9          8
                              4 5 6
                              7 8 9             3 2
                                          4 5 6 4
                                          7 8 9 7
                                                     5 6
                                                     8 9
  1     3   1 2               1 2 3 1 2 3                      1 2   3

  7
      5 6
      8 9
            4 5 6
              8     6         4 5 6 4 5 6
                              7 8 9 7 8 9   8 2 5              4 5
                                                               7 8
                                                                     6
                                                                     9
  1     3         1 2 3       1 2 3 1 2 3 1 2 3 1    2 3       1 2   3

  7     9
      5 6
      8 9
                  4 5 6
                  7 8 9                         8
                              4 5 6 4 5 6 4 5 6 4
                              7 8 9 7 8 9 7 8 9 7
                                                     5 6
                                                     8 9
                                                               4 5
                                                               7 8
                                                                     6
                                                                     9
  1     3                           1 2 3 1 2 3          1 2 3 1 2   3

  7     3 7 6
      5 6
      8 9                                     9
                                    4 5 6 4 5 6
                                    7 8 9 7 8 9
                                                         4 5 6 4 5
                                                         7 8 9 7 8
                                                                     6
                                                                     9
                1     2   3   1 2 3       1 2 3 1    2 3 1 2 3 1 2   3

      2 7     5 4
                7
                      5
                      8
                          6
                          9
                              4 5 6
                              7 8 9
                                          4 5 6 4
                                          7 8 9 7
                                                     5 6 4 5 6 4 5
                                                     8 9 7 8 9 7 8
                                                                     6
                                                                     9
  1     3 1 2   1     2   3   1 2 3             1    2 3 1 2 3 1 2   3

  7   8 9   8 1 4
      5 6 4 5 6 4
                7
                      5
                      8
                          6
                          9
                              4 5 6
                              7 8 9
                                                4
                                                7
                                                     5 6 4 5 6 4 5
                                                     8 9 7 8 9 7 8
                                                                     6
                                                                     9
  1     3 1 2   1     2   3   1 2 3 1 2 3 1 2 3          1 2 3

  7
      5 6 4 5 6 4
      8 9   8   7
                      5
                      8
                          6
                          9
                              4 5 6 4 5 6 4 5 6
                              7 8 9 7 8 9 7 8 9     6    4 5 6
                                                         7 8 9   4
      Back to Start           Skip Animation


                                               Helmut Simonis    Visualization Techniques   53
                                            Introduction
                            Visualization by Annotation
                                 Visualization Interface
                                           Conclusions


Propagation Steps (Forward Checking)
          1 2           1 2 3 1 2 3 1 2 3 1    2 3 1 2 3 1 2               3

      4     5 6
                  8     7
                          5 6
                            9 7
                                5 6
                                  9 7
                                      5 6
                                        9 7
                                               5 6
                                                 9 7
                                                     5 6
                                                       9 7
                                                           5               6
                                                                           9
        3   2     2 3                 2 3      2 3   2 3   2               3
      5 6 4 5 6 4 5 6
      8 9   8     8 9    1 7        4 5 6 4
                                      8 9
                                               5 6 4 5 6 4 5
                                               8 9   8 9   8
                                                                           6
                                                                           9
  1       1     1       1           1     1

  7
      5 6 4 5 6 4 5 6
        9       7   9   7  8
                        4 5 6
                            9
                                    4 5 6 4
                                    7     3 2
                                        9 7
                                               5 6
                                                 9
  1     3 1 2           1 2 3 1 2 3                                1   2   3

  7
      5 6 4 5 6
      8 9   8     6     4 5 6 4 5 6
                        7 8 9 7 8 9   8 2 5                        4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3       1 2 3   1 2 3 1 2 3 1 2 3 1    2 3                 1   2   3

  7     9
      5 6
      8 9
                4 5 6
                7 8 9                     8
                        4 5 6 4 5 6 4 5 6 4
                        7 8 9 7 8 9 7 8 9 7
                                               5 6
                                               8 9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3                     1 2 3 1 2 3              1   2   3   1   2   3

  7     3 7 6
      5 6
      8 9                               9
                              4 5 6 4 5 6
                              7 8 9 7 8 9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
                1 2 3   1 2 3       1 2 3 1    2   3   1   2   3   1   2   3

      2 7     5 4 5 6
                7 8 9
                        4 5 6
                        7 8 9
                                    4 5 6 4
                                    7 8 9 7
                                               5
                                               8
                                                   6
                                                   9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3   1 2 3             1    2   3   1   2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5 6
                7 8 9
                        4 5 6
                        7 8 9
                                          4
                                          7
                                               5
                                               8
                                                   6
                                                   9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3   1 2 3 1 2 3 1 2 3              1   2   3

  7
      5 6 4 5 6 4 5 6
      8 9   8   7 8 9
                        4 5 6 4 5 6 4 5 6
                        7 8 9 7 8 9 7 8 9     6        4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9       4
      Back to Start     Skip Animation


                                         Helmut Simonis                Visualization Techniques   54
                                            Introduction
                            Visualization by Annotation
                                 Visualization Interface
                                           Conclusions


Propagation Steps (Forward Checking)
          1 2           1 2 3 1 2 3 1 2 3 1    2 3 1 2 3 1 2               3

      4     5 6
                  8     7
                          5 6
                            9 7
                                5 6
                                  9 7
                                      5 6
                                        9 7
                                               5 6
                                                 9 7
                                                     5 6
                                                       9 7
                                                           5               6
                                                                           9
        3   2     2 3                 2 3      2 3   2 3   2               3
      5 6 4 5 6 4 5
      8 9   8       9    1 7        4 5 6 4
                                      8 9
                                               5 6 4 5 6 4 5
                                               8 9   8 9   8
                                                                           6
                                                                           9
  1       1     1       1           1     1

  7
      5 6 4 5 6 4 5
        9           9   7  8
                        4 5 6
                            9
                                    4 5 6 4
                                    7     3 2
                                        9 7
                                               5 6
                                                 9
  1     3 1 2           1 2 3 1 2 3                                1   2   3

  7
      5 6 4 5 6
      8 9   8     6     4 5 6 4 5 6
                        7 8 9 7 8 9   8 2 5                        4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3       1 2 3   1 2 3 1 2 3 1 2 3 1    2 3                 1   2   3

  7     9
      5 6
      8 9
                4 5
                    9                     8
                        4 5 6 4 5 6 4 5 6 4
                        7 8 9 7 8 9 7 8 9 7
                                               5 6
                                               8 9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3                     1 2 3 1 2 3              1   2   3   1   2   3

  7     3 7 6
      5 6
      8 9                               9
                              4 5 6 4 5 6
                              7 8 9 7 8 9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
                1 2 3   1 2 3       1 2 3 1    2   3   1   2   3   1   2   3

      2 7     5 4 5
                    9
                        4 5 6
                        7 8 9
                                    4 5 6 4
                                    7 8 9 7
                                               5
                                               8
                                                   6
                                                   9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3   1 2 3             1    2   3   1   2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5
                    9
                        4 5 6
                        7 8 9
                                          4
                                          7
                                               5
                                               8
                                                   6
                                                   9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3   1 2 3 1 2 3 1 2 3              1   2   3

  7
      5 6 4 5 6 4 5
      8 9   8       9
                        4 5 6 4 5 6 4 5 6
                        7 8 9 7 8 9 7 8 9     6        4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9       4
      Back to Start     Skip Animation


                                         Helmut Simonis                Visualization Techniques   55
                                            Introduction
                            Visualization by Annotation
                                 Visualization Interface
                                           Conclusions


Propagation Steps (Forward Checking)
          1 2           1 2 3 1 2 3 1 2 3 1    2 3 1 2 3 1 2               3

      4     5 6
                  8     7
                          5 6
                            9 7
                                5 6
                                  9 7
                                      5 6
                                        9 7
                                               5 6
                                                 9 7
                                                     5 6
                                                       9 7
                                                           5               6
                                                                           9
        3   2     2 3                 2 3      2 3   2 3   2               3
      5 6 4 5 6 4 5
      8 9   8       9    1 7        4 5 6 4
                                      8 9
                                               5 6 4 5 6 4 5
                                               8 9   8 9   8
                                                                           6
                                                                           9
  1       1     1       1           1     1

  7
      5 6 4 5 6 4 5
        9           9   7  8
                        4 5 6
                            9
                                    4 5 6 4
                                    7     3 2
                                        9 7
                                               5 6
                                                 9
  1     3 1             1   3 1   3                                1       3

  7     9
          4
                  6     4
                        7
                              4
                            9 7   9   8 2 5                        4
                                                                   7       9
  1     3       1 2 3   1 2 3 1 2 3 1 2 3 1    2 3                 1   2   3

  7     9
      5 6
      8 9
                4 5
                    9                     8
                        4 5 6 4 5 6 4 5 6 4
                        7 8 9 7 8 9 7 8 9 7
                                               5 6
                                               8 9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3                     1 2 3 1 2 3              1   2   3   1   2   3

  7     3 7 6
      5 6
      8 9                               9
                              4 5 6 4 5 6
                              7 8 9 7 8 9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
                1 2 3   1 2 3       1 2 3 1    2   3   1   2   3   1   2   3

      2 7     5 4 5
                    9
                        4 5 6
                        7 8 9
                                    4 5 6 4
                                    7 8 9 7
                                               5
                                               8
                                                   6
                                                   9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3   1 2 3             1    2   3   1   2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5
                    9
                        4 5 6
                        7 8 9
                                          4
                                          7
                                               5
                                               8
                                                   6
                                                   9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3   1 2 3 1 2 3 1 2 3              1   2   3

  7
      5 6 4 5 6 4 5
      8 9   8       9
                        4 5 6 4 5 6 4 5 6
                        7 8 9 7 8 9 7 8 9     6        4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9       4
      Back to Start     Skip Animation


                                         Helmut Simonis                Visualization Techniques   56
                                              Introduction
                              Visualization by Annotation
                                   Visualization Interface
                                             Conclusions


Propagation Steps (Forward Checking)
          1 2              2 3 1 2 3 1 2 3     1 2     3 1 2 3 1 2             3

      4     5 6
                  8   7
                           5
                             9 7
                                 5 6
                                   9 7
                                       5 6
                                         9     7
                                                 5     6
                                                       9 7
                                                           5 6
                                                             9 7
                                                                 5             6
                                                                               9
        3   2     2 3                  2 3       2     3   2 3   2             3
      5 6 4 5 6 4 5
      8 9   8       9     1 7        4 5 6
                                       8 9
                                               4 5
                                                 8
                                                       6 4 5 6 4 5
                                                       9   8 9   8
                                                                               6
                                                                               9
  1       1     1                    1         1

  7
      5 6 4 5 6 4 5
        9
                      4
                    9 7
                           5
                            89
                                     4 5 6
                                     7   9  3 24 5
                                               7
                                                       6
                                                       9
  1     3 1                  3 1   3                                   1       3

  7     9
          4
                  6   4
                      7
                               4
                             9 7   9    8 2 5                          4
                                                                       7       9
  1     3       1 2 3      2 3 1 2 3 1 2 3     1 2 3                   1   2   3

  7     9
      5 6
      8 9
                4 5   4
                    9 7
                           5   4 5 6 4 5 6
                           8 9 7 8 9 7 8 9  8  4 5 6
                                               7 8 9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3                      1 2 3 1 2 3                 1   2   3   1   2   3

  7     3 7 6
      5 6
      8 9
                               4 5 6 4 5 6
                               7 8 9 7 8 99                4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
                1 2 3      2 3       1 2 3     1   2   3   1   2   3   1   2   3

      2 7     5 4 5   4
                    9 7
                           5
                           8 9
                                     4 5 6
                                     7 8 9
                                               4
                                               7
                                                   5
                                                   8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3      2 3                 1   2   3   1   2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5   4
                    9 7
                           5
                           8 9
                                               4
                                               7
                                                   5
                                                   8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3      2 3 1 2 3 1 2 3                 1   2   3

  7
      5 6 4 5 6 4 5
      8 9   8
                      4
                    9 7
                           5   4 5 6 4 5 6
                           8 9 7 8 9 7 8 9         6       4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9       4
      Back to Start       Skip Animation


                                           Helmut Simonis                  Visualization Techniques   57
                                              Introduction
                              Visualization by Annotation
                                   Visualization Interface
                                             Conclusions


Propagation Steps (Forward Checking)
          1 2              2 3 1 2 3 1 2 3     1 2     3 1 2 3 1 2             3

      4     5 6
                  8   7
                           5
                             9 7
                                 5 6
                                   9 7
                                       5 6
                                         9     7
                                                 5     6
                                                       9 7
                                                           5 6
                                                             9 7
                                                                 5             6
                                                                               9
        3   2     2 3                  2 3       2     3   2 3   2             3
      5 6 4 5 6 4 5
      8 9   8       9     1 7        4 5 6
                                       8 9
                                               4 5
                                                 8
                                                       6 4 5 6 4 5
                                                       9   8 9   8
                                                                               6
                                                                               9
  1       1     1                    1         1

  7
      5 6 4 5 6 4 5
        9
                      4
                    9 7
                           5
                            89
                                     4 5 6
                                     7   9  3 24 5
                                               7
                                                       6
                                                       9
  1     3 1                  3 1   3                                   1       3

  7     9
          4
                  6   4
                      7
                               4
                             9 7   9    8 2 5                          4
                                                                       7     9
  1     3       1 2 3      2 3 1 2 3 1 2 3     1 2 3                   1   2 3

  7     9
      5 6       4 5   4
                      7
                           5   4 5 6 4 5 6
                               7     7      8  4 5 6
                                               7
                                                                       4
                                                                       7
                                                                           5 6

  1     3                      1 2 3 1 2 3                 1   2   3   1   2   3

  7     3 7 6
      5 6
      8 9
                               4 5 6 4 5 6
                               7 8 9 7 8 99                4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
                1 2 3      2 3       1 2 3     1   2   3   1   2   3   1   2   3

      2 7     5 4 5   4
                    9 7
                           5
                           8 9
                                     4 5 6
                                     7 8 9
                                               4
                                               7
                                                   5
                                                   8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3      2 3                 1   2   3   1   2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5   4
                    9 7
                           5
                           8 9
                                               4
                                               7
                                                   5
                                                   8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3      2 3 1 2 3 1 2 3                 1   2   3

  7
      5 6 4 5 6 4 5
      8 9   8
                      4
                    9 7
                           5   4 5 6 4 5 6
                           8 9 7 8 9 7 8 9         6       4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9       4
      Back to Start       Skip Animation


                                           Helmut Simonis                  Visualization Techniques   58
                                              Introduction
                              Visualization by Annotation
                                   Visualization Interface
                                             Conclusions


Propagation Steps (Forward Checking)
          1 2              2 3       2 3 1 2 3   1 2   3 1 2 3 1 2             3

      4     5 6
                  8   7
                           5
                             9
                                       6
                                       9 7
                                           5 6
                                             9   7
                                                   5   6
                                                       9 7
                                                           5 6
                                                             9 7
                                                                 5             6
                                                                               9
        3   2     2 3                      2 3     2   3   2 3   2             3
      5 6 4 5 6 4 5
      8 9   8       9     1 7            4 5 6
                                           8 9
                                                 4 5
                                                   8
                                                       6 4 5 6 4 5
                                                       9   8 9   8
                                                                               6
                                                                               9
  1       1     1                        1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7     89
                                         4 5 6
                                         7   93 24 5
                                                 7
                                                       6
                                                       9
  1     3 1                  3         3                               1       3

  7     9
          4
                  6   4
                      7      9
                                 4
                                   9      8 2 5                        4
                                                                       7     9
  1     3       1 2 3   2    3   2 3 1 2 3 1 2         3               1   2 3

  7     9
      5 6       4 5   4 5
                      7
                               4   6 4 5
                                     7
                                         6 4 5
                                           7  8        6               4
                                                                       7
                                                                           5 6

  1     3                        2 3 1 2 3                 1   2   3   1   2   3

  7     3 7 6
      5 6
      8 9
                               4   6 4 5
                                   9 7 8
                                         6
                                         9  9              4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
                1 2 3   2    3       1 2 3 1 2         3   1   2   3   1   2   3

      2 7     5 4 5   4 5
                    9 7 8    9
                                     4 5
                                     7 8
                                         6 4 5
                                         9 7 8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3   2    3             1 2         3   1   2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5   4 5
                    9 7 8    9
                                           4 5
                                           7 8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3   2    3   2 3 1 2 3                 1   2   3

  7
      5 6 4 5 6 4 5
      8 9   8
                      4 5
                    9 7 8    9
                               4   6 4 5 6
                                   9 7 8 9        6        4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9       4
      Back to Start       Skip Animation


                                           Helmut Simonis                  Visualization Techniques   59
                                                Introduction
                                Visualization by Annotation
                                     Visualization Interface
                                               Conclusions


Propagation Steps (Forward Checking)
          1 2                2 3       2 3 1 2 3   1 2   3 1 2 3 1 2           3

      4     5 6
                  8     7
                             5
                               9
                                         6
                                         9 7
                                             5 6
                                               9   7
                                                     5   6
                                                         9 7
                                                             5 6
                                                               9 7
                                                                   5           6
                                                                               9
        3   2     2 3                        2 3     2   3   2 3   2           3
      5 6 4 5 6 4 5
      8 9   8       9       1 7            4 5 6
                                             8 9
                                                   4 5
                                                     8
                                                         6 4 5 6 4 5
                                                         9   8 9   8
                                                                               6
                                                                               9
  1       1     1                          1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7       89
                                           4 5 6
                                           7   93 24 5
                                                   7
                                                         6
                                                         9
  1     3 1                    3         3                             1       3

  7     9
          4
                  6   4
                      7        9  9
                                   4
                                            8 2 5                      4
                                                                       7     9
  1     3       1 2 3   2      32 3 1 2        3 1 2 3                 1   2 3

  7     9
      5 6       4 5   4 5
                      7
                              4   6 4 5
                                    7           8
                                               6 4 5 6
                                                 7
                                                                       4
                                                                       7
                                                                           5 6

  1                             2   1 2                      1 2       1   2
      5
      8 3 7 6                 4     4 5
                                      8       9              4 5
                                                               8
                                                                       4   5
                                                                           8
                1 2 3     2 3       1 2        3 1 2 3       1 2   3   1   2   3

      2 7     5 4 5
                    9
                        4 5
                        7 8 9
                                    4 5
                                    7 8
                                               6 4 5 6
                                               9 7 8 9
                                                             4 5
                                                             7 8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3     2 3                    1 2 3       1 2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5
                    9
                        4 5
                        7 8 9
                                                 4 5 6
                                                 7 8 9
                                                             4 5
                                                             7 8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3     2 3   2 3 1 2        3             1 2   3

  7
      5 6 4 5 6 4 5
      8 9   8       9
                        4 5
                        7 8 9
                              4   6 4 5
                                  9 7 8
                                               6
                                               9    6        4 5
                                                             7 8
                                                                   6
                                                                   9       4
      Back to Start         Skip Animation


                                             Helmut Simonis                Visualization Techniques   60
                                               Introduction
                               Visualization by Annotation
                                    Visualization Interface
                                              Conclusions


Propagation Steps (Forward Checking)
          1 2              2 3         2 3 1 2 3   1 2   3 1 2 3 1 2       3

      4     5 6
                  8   7
                           5
                             9
                                         6
                                         9 7
                                             5 6
                                               9   7
                                                     5   6
                                                         9 7
                                                             5 6
                                                               9 7
                                                                   5       6
                                                                           9
        3   2     2 3                        2 3     2   3   2 3   2       3
      5 6 4 5 6 4 5
      8 9   8       9     1 7                5 6
                                               9
                                                   4 5
                                                     8
                                                         6 4 5 6 4 5
                                                         9   8 9   8
                                                                           6
                                                                           9
  1       1     1                          1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7     8  9           7
                                             5 6
                                               93 24 5
                                                   7
                                                         6
                                                         9
  1     3 1                    3         3                         1       3

  7     9
          4
                  6   4
                      7        9
                                   4
                                       9    8 2 5                  4
                                                                   7     9
  1     3       1 2 3   2      3     2 3 1 2 3 1 2 3               1   2 3

  7     9
      5 6       4 5   4 5
                      7
                                   4   6
                                         7      8
                                           5 6 4 5 6
                                               7
                                                                   4
                                                                   7
                                                                       5 6

  1                                  2   1 2         1 2           1   2
      5
      8 3 7 6                      4       5
                                              9      4 5
                                                       8
                                                                   4   5
                                                                       8
                1 2 3      2   3         1 2 3 1 2 3 1 2       3   1   2   3

      2 7     5 4 5   4
                    9 7
                           5
                           8   9         7
                                           5 6 4 5 6 4 5
                                             9 7 8 9 7 8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3      2   3               1 2 3 1 2       3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5   4
                    9 7
                           5
                           8   9
                                               4 5 6 4 5
                                               7 8 9 7 8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3      2   3     2 3 1 2 3       1 2       3

  7
      5 6 4 5 6 4 5
      8 9   8
                      4
                    9 7
                           5
                           8   9
                                   4   6
                                       9 7
                                           5 6
                                             9      64 5
                                                     7 8
                                                               6
                                                               9       4
      Back to Start       Skip Animation


                                             Helmut Simonis            Visualization Techniques   61
                                                       Introduction
                                       Visualization by Annotation
                                            Visualization Interface
                                                      Conclusions


Propagation Steps (Forward Checking)
          1 2                      2 3         2 3 1 2 3   1 2   3 1 2 3 1 2       3

      4     5 6
                      8       7
                                   5
                                     9
                                                 6
                                                 9 7
                                                     5 6
                                                       9   7
                                                             5   6
                                                                 9 7
                                                                     5 6
                                                                       9 7
                                                                           5       6
                                                                                   9
        3   2     2 3                                2 3     2   3   2 3   2       3
      5 6 4 5 6 4 5
      8 9   8       9             1 7                5 6
                                                       9
                                                           4 5
                                                             8
                                                                 6 4 5 6 4 5
                                                                 9   8 9   8
                                                                                   6
                                                                                   9
  1       1     1                                  1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7             8  9           7
                                                     5 6
                                                       93 24 5
                                                           7
                                                                 6
                                                                 9
  1     3 1                            3         3                         1       3

  7     9
          4
                      6
                      4
                      7                9
                                           4
                                               9    8 2 5                  4
                                                                           7     9
  1     3       1 2 3   2              3     2 3 1 2 3 1 2 3               1   2 3

  7     9
      5 6       4 5   4 5
                      7
                                           4   6
                                                 7      8
                                                   5 6 4 5 6
                                                       7
                                                                           4
                                                                           7
                                                                               5 6

  1                                          2   1 2         1 2           1   2
      5
      8 3 7 6                              4       5
                                                      9      4 5
                                                               8
                                                                           4   5
                                                                               8
                  1       3            3         1   3 1   3 1         3   1       3

      2 7     5   4
                        9
                              4
                                   8   9
                                                     6 4
                                                     9
                                                           6 4
                                                         8 9   8
                                                                       6
                                                                       9
                                                                           4
                                                                             8
                                                                                   6
                                                                                   9
  1   3   1 2     1   2 3          2   3               1 2 3 1 2       3   1 2     3
    5 6
  7 8 9     8 1 4
          4 5 6   4   5
                        9
                              4
                              7
                                   5
                                   8   9
                                                       4 5 6 4 5
                                                       7 8 9 7 8
                                                                       6
                                                                       9
                                                                           4 5
                                                                           7 8
                                                                                   6
                                                                                   9
  1   3   1 2     1   2 3          2   3     2 3 1 2 3       1 2       3
    5 6
  7 8 9
          4 5 6
            8
                  4   5
                        9
                              4
                              7
                                   5
                                   8   9
                                           4   6
                                               9 7
                                                   5 6
                                                     9      64 5
                                                             7 8
                                                                       6
                                                                       9       4
      Back to Start               Skip Animation


                                                     Helmut Simonis            Visualization Techniques   62
                                                       Introduction
                                       Visualization by Annotation
                                            Visualization Interface
                                                      Conclusions


Propagation Steps (Forward Checking)
          1 2                      2 3         2 3 1 2 3   1   3 1 2   3 1 2 3

      4     5 6
                      8       7
                                   5
                                     9
                                                 6
                                                 9 7
                                                     5 6
                                                       9   7
                                                               5
                                                                 7
                                                                   5   6
                                                                       9 7
                                                                           5 6
                                                                             9
        3   2     2 3                                2 3       3   2   3   2 3
      5 6 4 5 6 4 5
      8 9   8       9             1 7                5 6
                                                       9
                                                           4 5
                                                             8
                                                                 4 5
                                                                   8
                                                                       6 4 5 6
                                                                       9   8 9
  1       1     1                                  1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7             8  9           7
                                                     5 6
                                                       93 24 5
                                                           7
  1     3 1                            3         3                         1       3

  7     9
          4
                      6
                      4
                      7                9
                                           4
                                               9    8 2 5                  4
                                                                           7     9
  1     3       1 2 3   2              3     2 3 1 2 3 1   3               1   2 3

  7     9
      5 6       4 5   4 5
                      7
                                           4   6
                                                 7      8
                                                   5 6 4 5
                                                       7
                                                                           4
                                                                           7
                                                                               5 6

  1                                          2   1 2         1 2           1   2
      5
      8 3 7 6                              4       5
                                                      9      4 5
                                                               8
                                                                           4   5
                                                                               8
                  1       3            3         1   3 1   3 1         3   1       3

      2 7     5   4
                        9
                              4
                                   8   9
                                                     6 4
                                                     9   8
                                                             4
                                                               8
                                                                       6
                                                                       9
                                                                           4
                                                                             8
                                                                                   6
                                                                                   9
  1   3   1 2     1   2 3          2   3               1   3 1 2       3   1 2     3
    5 6
  7 8 9       1 4
          4 5 6
            8
                  4   5
                        9
                              4
                              7
                                   5
                                   8   9
                                                       4 5
                                                       7 8
                                                             4 5
                                                             7 8
                                                                       6
                                                                       9
                                                                           4 5
                                                                           7 8
                                                                                   6
                                                                                   9
  1   3   1 2     1   2 3          2   3     2 3 1 2 3       1 2       3
    5 6
  7 8 9
          4 5 6
            8
                  4   5
                        9
                              4
                              7
                                   5
                                   8   9
                                           4   6
                                               9 7
                                                   5 6
                                                     9         6
                                                             4 5
                                                             7 8
                                                                       6
                                                                       9       4
      Back to Start               Skip Animation


                                                     Helmut Simonis            Visualization Techniques   63
                                                      Introduction
                                      Visualization by Annotation
                                           Visualization Interface
                                                     Conclusions


Propagation Steps (Forward Checking)
          1 2                      2 3       2 3 1 2 3   1   3 1 2   3 1 2 3

      4     5 6
                      8       7
                                   5
                                     9
                                               6
                                               9 7
                                                   5 6
                                                     9   7
                                                             5
                                                               7
                                                                 5   6
                                                                     9 7
                                                                         5 6
                                                                           9
        3   2     2 3                              2 3       3   2   3   2 3
      5 6 4 5 6 4 5
      8 9   8       9             1 7              5 6
                                                     9
                                                         4 5
                                                           8
                                                               4 5
                                                                 8
                                                                     6 4 5 6
                                                                     9   8 9
  1       1     1                                1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7             89           7
                                                   5 6
                                                     93 24 5
                                                         7
  1     3 1                          3         3                       1       3

  7     9
          4
                      6
                      4
                      7              9
                                         4
                                             9    8 2 5                4
                                                                       7     9
  1     3       1 2 3   2            3     2 3 1 2 3 1   3             1   2 3

  7     9
      5 6       4 5   4 5
                      7
                                         4   6
                                               7      8
                                                 5 6 4 5
                                                     7
                                                                       4
                                                                       7
                                                                           5 6

  1                                        2   1 2         1 2         1   2
      5
      8 3 7 6                            4       5
                                                    9      4 5
                                                             8
                                                                       4   5
                                                                           8
                  1     3 3                    1   3 1   3 1         3 1   3

      2 7     5   4
                  9
                    4
                      8 9
                                                   6 4
                                                   9   8
                                                           4
                                                             8
                                                                     6 4
                                                                     9
                                                                           6
                                                                         8 9
      3   2     2 3   2 3                                3   2       3   2 3
    5 6
  7 8 9
          5 6
          8   1 4
                5     5
                  9 7 8 9
                                                       5
                                                     7 8
                                                             5
                                                           7 8
                                                                     6   5 6
                                                                     9 7 8 9
  1   3 1 2   1 2 3   2 3                  2 3 1 2 3       1 2       3
    5 6 4 5 6 4 5
  7 8 9   8
                    4 5
                  9 7 8 9
                                         4   6
                                             9 7
                                                 5 6
                                                   9         6
                                                           4 5
                                                           7 8
                                                                     6
                                                                     9     4
      Back to Start               Skip Animation


                                                   Helmut Simonis          Visualization Techniques   64
                                                      Introduction
                                      Visualization by Annotation
                                           Visualization Interface
                                                     Conclusions


Propagation Steps (Forward Checking)
          1 2                      2 3       2 3 1 2 3   1           1 2 3
                                                                 3 1 2

      4     5 6
                      8       7
                                   5
                                     9
                                               6
                                               9 7
                                                   5 6
                                                     9   7
                                                             5     6
                                                                   9 7
                                                                   7
                                                                       5 6
                                                                         9
        3   2     2 3                              2 3       3   2     2 3
      5 6 4 5 6 4 5
      8 9   8       9             1 7              5 6
                                                     9
                                                         4 5
                                                           8
                                                               4   6 4 5 6
                                                                   9   8 9
  1       1     1                                1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7             89           7
                                                   5 6
                                                     93 24 5
                                                         7
  1     3 1                          3         3                     1   3

  7     9
          4
                      6
                      4
                      7              9
                                         4
                                             9    8 2 5              4
                                                                     7   9
  1     3       1 2 3   2            3     2 3 1 2 3     1   3       1 2 3

  7     9
      5 6       4 5   4 5
                      7
                                         4   6
                                               7
                                                 5 6
                                                      8  4 5
                                                         7
                                                                     4 5 6
                                                                     7
  1                                        2   1 2             1 2   1 2
      5
      8 3 7 6                            4       5
                                                    9          4     4 5
                                                                       8
                  1     3 3     1   3                    1   3 1     1   3

      2 7     5   4
                  9
                    4
                      8 9
                                    6
                                    9
                                                         4
                                                           8
                                                               4   6 4
                                                                   9
                                                                         6
                                                                       8 9
      3   2     2 3   2 3                                    3   2     2 3
    5 6
  7 8 9
          5 6
          8   1 4
                5     5
                  9 7 8 9
                                                           5
                                                         7 8   7
                                                                   6   5 6
                                                                   9 7 8 9
  1   3 1 2   1 2 3   2 3   2 3 1 2 3                          1 2
    5 6 4 5 6 4 5
  7 8 9   8
                    4 5
                  9 7 8 9
                          4   6
                              9 7
                                  5 6
                                    9                        6 4
                                                               7
                                                                   6
                                                                   9     4
      Back to Start               Skip Animation


                                                   Helmut Simonis        Visualization Techniques   65
                                                        Introduction
                                        Visualization by Annotation
                                             Visualization Interface
                                                       Conclusions


Propagation Steps (Forward Checking)
            1 2                      2 3       2 3 1 2 3     1           1 2 3
                                                                     3 1 2

      4       5 6
                        8       7
                                     5
                                       9
                                                 6
                                                 9 7
                                                     5 6
                                                       9     7
                                                                 5     6
                                                                       9 7
                                                                       7
                                                                           5 6
                                                                             9
        3   2     2 3                                2 3         3   2     2 3
      5 6 4 5 6 4 5
      8 9   8       9               1 7              5 6
                                                       9
                                                             4 5
                                                               8
                                                                   4   6 4 5 6
                                                                       9   8 9
  1       1     1                                  1         1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7               89           7
                                                     5 6
                                                       9   3 2
                                                             4 5
                                                             7
  1     3 1                            3         3                       1   3

  7     9
          4           4
                      7 6              9
                                           4
                                               9       8 2 5             4
                                                                         7   9
  1     3       1 2 3   2              3     2 3 1 2 3       1   3       1 2 3

  7     9
      5 6       4 5   4 5
                      7
                                           4   6
                                                 7
                                                   5 6
                                                           8 4 5
                                                             7
                                                                         4 5 6
                                                                         7
  1                                          2   1 2               1 2   1 2
      5
      8 3 7 6                              4       5
                                                         9         4     4 5
                                                                           8
                    1       3
                            3                      1     3   1   3 1     1   3

      2 7     5     4
                      9
                        4
                          8 9
                                                         6
                                                         9
                                                             4
                                                               8
                                                                   4   6 4
                                                                       9
                                                                             6
                                                                           8 9
          3   2     2 3   2 3                                    3   2     2 3
    5
  7 8
          6
          9   1 4
              5 6
              8
                    5     5
                      9 7 8 9
                                                               5
                                                             7 8   7
                                                                       6   5 6
                                                                       9 7 8 9
  1       3 1 2   1 2 3   2 3                  2 3 1 2 3           1 2
    5
  7 8     9
              5
              8
                    5     5
                      9 7 8 9                    9 7
                                                     5
                                                       9         6     7     9   4
      Back to Start                 Skip Animation


                                                       Helmut Simonis            Visualization Techniques   66
                                                        Introduction
                                        Visualization by Annotation
                                             Visualization Interface
                                                       Conclusions


Propagation Steps (Forward Checking)
            1 2                      2 3       2 3 1 2 3   1           1
                                                                   3 1 2   3

      4       5 6
                        8       7
                                     5
                                       9
                                                 6
                                                 9 7
                                                     5 6
                                                       9   7
                                                               5     6
                                                                     9 7
                                                                     7
                                                                         5 6
                                                                           9
        3   2     2 3                                2 3       3   2       3
      5 6 4 5 6 4 5
      8 9   8       9               1 7              5 6
                                                       9
                                                           4 5
                                                             8
                                                                 4   6
                                                                     9
                                                                         5 6
                                                                         8 9
  1       1     1                                  1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7               89           7
                                                     5 6
                                                       9   3 2
                                                           4 5
                                                           7
  1     3 1                            3         3                     1   3

  7     9
          4           4
                      7 6              9
                                           4
                                               9       8 2 5               7     9
  1     3       1 2 3   2              3     2 3 1 2 3 1   3               1     3

  7     9
      5 6       4 5   4 5
                      7
                                           4   6
                                                 7
                                                   5 6 4 5
                                                       7   8               7
                                                                               5 6

  1                                          2   1 2         1 2           1
      5
      8 3 7 6                              4       5
                                                         9   4         5
                                                                       8
                    1       3          3           1   3 1   3 1     1   3

      2 7     5     4
                      9
                        4
                          8 9
                                                       6 4
                                                       9   8
                                                               4   6
                                                                   9
                                                                         6
                                                                       8 9
          3   2     2 3   2 3                                3   2       3
    5
  7 8
          6
          9   1 4
              5 6
              8
                    5     5
                      9 7 8 9
                                                           5
                                                         7 8   7
                                                                   6   5 6
                                                                   9 7 8 9
  1       3 1 2   1 2 3   2 3                  2 3 1 2 3       1 2
    5
  7 8     9
              5
              8
                    5     5
                      9 7 8 9                    9 7
                                                     5
                                                       9       6
                                                               7   9           4
      Back to Start                 Skip Animation


                                                       Helmut Simonis          Visualization Techniques   67
                                                        Introduction
                                        Visualization by Annotation
                                             Visualization Interface
                                                       Conclusions


Propagation Steps (Forward Checking)
            1 2                      2 3    2 3 1 2 3    1           1
                                                                 3 1 2   3

      4       5 6
                          8     7
                                     5
                                       9
                                              6
                                              9 7
                                                  5 6
                                                    9    7
                                                             5     6
                                                                   9 7
                                                                   7
                                                                       5 6
                                                                         9
        3       2         2 3                     2 3        3   2       3
      5 6
        9
                5 6       5
                            9       1 7           5 6
                                                    9
                                                         4 5
                                                           8
                                                               4   6
                                                                   9
                                                                       5 6
                                                                       8 9
  1         1         1                         1        1

  7
    5 6
      9
          5 6   5   4 5
                  9 7   9             8         7
                                                  5 6
                                                    9 3 24 5
                                                         7
  1   3 1               3                     3                      1   3

  7   9
        4           4
                    7   9 6
                          4
                              9                   8 2 5                  7     9
  1   3       1 2 3   2 3   2 3 1 2 3 1   3                              1     3

  7
    5 6
        9     4 5   4 5
                    7
                          4   6
                                7
                                  5 6 4 5
                                      7               8                  7
                                                                             5 6

  1                         2   1 2         1 2                          1
    5
    8   3 7 6             4       5         4
                                                    9                        5
                                                                             8
              1   3     3       1   3 1   3 1                            1   3

      2 7     5
              4
                  9
                    4
                      8 9
                                    6 4
                                    9   8
                                            4   6
                                                9
                                                                             6
                                                                           8 9
      3   2     2 3   2 3                 3   2                              3
    5 6
  7 8 9
          5 6
          8   1 4
                5     5
                  9 7 8 9
                                        5
                                      7 8   7
                                                6
                                                9
                                                                           5 6
                                                                         7 8 9
  1   3 1 2   1 2 3   2 3   2 3 1 2 3       1 2
    5
  7 8 9
          5
          8
                5     5
                  9 7 8 9     9 7
                                  5
                                    9       7   9            6               4
      Back to Start                 Skip Animation


                                                     Helmut Simonis          Visualization Techniques   68
                                                    Introduction
                                    Visualization by Annotation
                                         Visualization Interface
                                                   Conclusions


Propagation Steps (Forward Checking)
            1 2                  2 3    2 3      2 3 1   3 1 2   1   3

      4       5 6
                          8      5
                                   9
                                          6
                                          9
                                                 5 6
                                                   9 7
                                                       5
                                                           7
                                                               6
                                                               9 7
                                                                   5 6
                                                                     9
        3       2         2 3                    2 3     3   2       3
      5 6
        9
                5 6       5
                            9   1 7              5 6 4 5
                                                   9   8
                                                           4   6
                                                               9
                                                                   5 6
                                                                   8 9
  1         1         1                              1

  7
    5 6
      9
          5 6   5
                  9
                    4 5
                        9         8               3 2
                                                 5 6 4 5
                                                   9 7
  1   3 1               3     3                                  1   3

  7   9
        4           4
                    7   9 6
                          4
                              9               8 2 5                7     9
  1   3       1 2 3   2 3   2 3 1 2 3 1   3                        1     3

  7
    5 6
        9     4 5   4 5
                    7
                          4   6
                                7
                                  5 6 4 5
                                      7           8                7
                                                                       5 6

  1                         2   1 2         1 2                    1
    5
    8   3 7 6             4       5         4
                                                9                      5
                                                                       8
              1   3     3       1   3 1   3 1                      1   3

      2 7     5
              4
                  9
                    4
                      8 9
                                    6 4
                                    9   8
                                            4   6
                                                9
                                                                       6
                                                                     8 9
      3   2     2 3   2 3                 3   2                        3
    5 6
  7 8 9
          5 6
          8   1 4
                5     5
                  9 7 8 9
                                        5
                                      7 8   7
                                                6
                                                9
                                                                     5 6
                                                                   7 8 9
  1   3 1 2   1 2 3   2 3   2 3 1 2 3       1 2
    5
  7 8 9
          5
          8
                5     5
                  9 7 8 9     9 7
                                  5
                                    9       7   9     6                4
      Back to Start             Skip Animation


                                                 Helmut Simonis        Visualization Techniques   69
                                                          Introduction
                                          Visualization by Annotation
                                               Visualization Interface
                                                         Conclusions


Propagation Steps (Forward Checking)
            1 2                        2 3       2 3       2 3 1     1        1

      4       5 6
                          8            5
                                         9
                                                   6
                                                   9
                                                           5 6
                                                             9 7
                                                                 5
                                                                     7
                                                                            6
                                                                            9 7
                                                                                5 6
                                                                                  9
        3       2         2 3                              2 3
      5 6
        9
                5 6       5
                            9         1 7                  5 6 4 5
                                                             9   8
                                                                     4      6
                                                                            9
                                                                                    5 6
                                                                                    8 9
  1         1         1                                        1

  7
      5 6
        9
                5 6       5
                              9
                                  4 5
                                        89                     3 2
                                                           5 6 4 5
                                                             9 7
                                         3         3                            1       3

      1         4 6               4
                                  7   9     9
                                             4
                                                           8 2 5                7     9
                                    2 3   2 3 1            2 3 1   3            1     3

      5         9 2               4 5
                                  7
                                        4   6
                                              7                8
                                                           5 6 4 5
                                                               7                7
                                                                                    5 6

                                          2   1            2         1 2        1

      8         3 7 6                   4                  5
                                                             9       4   5
                                                                         8
                      1       3          3             1 3 1   3 1     1   3

      2         7     5
                      4
                      9
                        4
                          8 9
                                                         6 4
                                                         9   8
                                                                 4   6
                                                                     9
                                                                           6
                                                                         8 9
          3   2     2 3   2 3                                  3   2       3
    5
  7 8
          6
          9
              5 6
              8
                    5
                      1 4 5
                      9 7 8 9
                                                             5
                                                           7 8   7
                                                                     6   5 6
                                                                     9 7 8 9
  1       3 1 2   1 2 3   2 3                    2 3 1 2 3       1 2
    5
  7 8     9
              5
              8
                    5     5
                      9 7 8 9                      9 7
                                                       5
                                                         9      67   9              4
      Back to Start                   Skip Animation


                                                           Helmut Simonis           Visualization Techniques   70
                                                            Introduction
                                            Visualization by Annotation
                                                 Visualization Interface
                                                           Conclusions


Propagation Steps (Forward Checking)
              1 2                        2 3     2 3       2 3 1         1       1

      4         5 6
                            8            5
                                           9
                                                   6
                                                   9
                                                           5 6
                                                             9 7
                                                                 5
                                                                         7
                                                                               6
                                                                               9 7
                                                                                   5 6
                                                                                     9
          3       2             3                          2 3
          6
          9
                  5 6       5
                                9       1 7                5 6 4 5
                                                             9   8
                                                                         4     6
                                                                               9
                                                                                       5 6
                                                                                       8 9
              1         1                                      1

  7
          6
          9
                  5 6       5
                                9
                                    4 5
                                          89                   3 2
                                                           5 6 4 5
                                                             9 7
                                           3       3                                       3

      1           4 6               7      9       9       8 2 5                   7       9
                                           3       3 1   3 1         3             1       3

      5           9 2               4
                                    7
                                               4   6
                                                     7
                                                         6 4
                                                           7   8                   7
                                                                                           6

                                                 2   1 2                 1 2       1

      8           3 7 6                        4       5
                                                             9           4             5

                        1       3          3           1 3 1   3 1     1   3

      2           7     5
                        4
                                9
                              8 9
                                    4                    6 4
                                                         9   8
                                                                 4   6
                                                                     9
                                                                           6
                                                                         8 9
          3       2           2 3
                                3                              3   2       3

  7
          6
          9
                  5 6
                  8     1 4
                        5     5
                          9 7 8 9
                                                             5
                                                           7 8   7
                                                                     6   5 6
                                                                     9 7 8 9
          3 1     2   1   3   2 3                2 3 1 2 3       1 2

  7       9
                  5
                  8
                        5     5
                          9 7 8 9                  9 7
                                                       5
                                                         9      67   9                 4
      Back to Start                     Skip Animation


                                                           Helmut Simonis              Visualization Techniques   71
                                                            Introduction
                                            Visualization by Annotation
                                                 Visualization Interface
                                                           Conclusions


Propagation Steps (Forward Checking)
              1 2                        2 3       2 3       2 3 1         1     1

      4         5 6
                            8            5
                                           9
                                                     6
                                                     9
                                                             5 6
                                                               9 7
                                                                   5
                                                                           7
                                                                               6
                                                                               9 7
                                                                                   5 6
                                                                                     9
          3       2             3                            2 3
          6
          9
                  5 6       5
                                9       1 7                  5 6 4 5
                                                               9   8
                                                                           4   6
                                                                               9
                                                                                       5 6
                                                                                       8 9
              1         1                                        1

  7
          6
          9         3 2
                  5 6       5
                                9
                                    4 5
                                          89
                                                             5 6 4 5
                                                               9 7
                                           3         3                                   3

      1 4 6     8 2 5               7      9         9                             7     9
                                           3         3 1       3 1     3           1     3

      5 9 2         8               4
                                    7
                                               4
                                                         7
                                                                 4
                                                                 7                 7
                                                                                         6




      8 3 7 6 2 5 9 4 1
                        1       3          3             1 3 1   3 1     1   3

      2 7     5         4
                          8     9
                                    4
                                           9
                                                           6 4
                                                           9   8
                                                                   4   6
                                                                       9
                                                                             6
                                                                           8 9
          3   2           2     3          3                     3   2       3

  7
          6
          9   1 4
              5 6
              8
                    5     5
                      9 7 8                9
                                                               5
                                                             7 8   7
                                                                       6   5 6
                                                                       9 7 8 9
          3 1 2   1   3   2                3       2 3 1 2 3       1 2

  7       9
              5
              8   6 5
                      4   5
                      9 7 8                9         9 7
                                                         5
                                                           9       7   9


      Back to Start                     Skip Animation


                                                             Helmut Simonis            Visualization Techniques   72
                                                            Introduction
                                            Visualization by Annotation
                                                 Visualization Interface
                                                           Conclusions


Propagation Steps (Forward Checking)
              1 2                        2 3       3       2 3 1         1

      4         5 6
                            8            5
                                           9
                                                   6
                                                   9
                                                             6
                                                             9 7
                                                                 5
                                                                         7
                                                                             6
                                                                             9 7
                                                                                 5 6
                                                                                   9
          3       2             3                          2 3
          6
          9
                  5 6       5
                                9       1 7                  6 4 5
                                                             9   8
                                                                             6
                                                                             9
                                                                                     5 6
                                                                                     8 9
              1         1                                      1

  7
          6
          9         3 2
                  5 6       5
                                9
                                    4 5
                                          89
                                                             6 4 5
                                                             9 7
                                           3       3                                   3

      1 4 6     8 2 5               7      9       9                             7
                                           3       3 1       3       3                 3

      5 9 2         8               4
                                    7
                                               4
                                                       7         7               7
                                                                                       6




      8 3 7 6 2 5 9 4 1
                        1       3          3           1 3 1   3 1         3

      2 7     5         4
                          8     9
                                    4
                                           9
                                                         6 4
                                                         9   8
                                                                     6
                                                                     9
                                                                           6
                                                                         8 9
          3   2           2     3          3                   3   2       3

  7
          6
          9   1 4
              5 6
              8
                    5     5
                      9 7 8                9
                                                             5
                                                           7 8   7
                                                                     6   5 6
                                                                     9 7 8 9
          3 1 2   1   3   2                3       3 1 2 3       1 2

  7       9
              5
              8   6 5
                      4   5
                      9 7 8                9       9 7       9           7   9


      Back to Start                     Skip Animation


                                                           Helmut Simonis            Visualization Techniques   73
                                                            Introduction
                                            Visualization by Annotation
                                                 Visualization Interface
                                                           Conclusions


Propagation Steps (Forward Checking)
              1 2                        2 3       3       2 3 1         1

      4         5 6
                            8            5
                                           9
                                                   6
                                                   9
                                                             6
                                                             9 7
                                                                 5
                                                                         7
                                                                             6
                                                                             9 7
                                                                                 5 6
                                                                                   9
          3       2             3                          2 3
          6
          9
                  5 6       5
                                9       1 7                  6 4 5
                                                             9   8
                                                                             6
                                                                             9
                                                                                     5 6
                                                                                     8 9
              1         1                                      1

  7
          6
          9         3 2
                  5 6       5
                                9
                                    4 5
                                          89
                                                             6 4 5
                                                             9 7
                                           3       3                                   3

      1 4 6     8 2 5               7      9       9                             7
                                           3       3 1       3       3                 3

      5 9 2         8               4
                                    7
                                               4
                                                       7         7               7
                                                                                       6




      8 3 7 6 2 5 9 4 1
                        1       3          3           1 3 1   3 1         3

      2 7     5         4
                          8     9
                                    4
                                           9
                                                         6 4
                                                         9   8
                                                                     6
                                                                     9
                                                                           6
                                                                         8 9
          3               2     3          3                   3   2       3
          6
          9   1 4
              5 6
              8
                    5     5
                      9 7 8                9
                                                             5
                                                           7 8   7
                                                                     6   5 6
                                                                     9 7 8 9
          3 1     1   3   2                3       3 1 2 3       1 2

          9
              5
              8   6 5
                      4   5
                      9 7 8                9       9 7       9           7   9


      Back to Start                     Skip Animation


                                                           Helmut Simonis            Visualization Techniques   74
                                                            Introduction
                                            Visualization by Annotation
                                                 Visualization Interface
                                                           Conclusions


Propagation Steps (Forward Checking)
              1 2                        2 3       3       2 3 1         1

      4         5 6
                            8            5
                                           9
                                                   6
                                                   9
                                                             6
                                                             9 7
                                                                 5
                                                                         7
                                                                             6
                                                                             9 7
                                                                                 5 6
                                                                                   9
          3       2             3                          2 3
          6
          9
                  5 6       5
                                9       1 7                  6 4 5
                                                             9   8
                                                                             6
                                                                             9
                                                                                     5 6
                                                                                     8 9
              1         1                                      1

  7
          6
          9         3 2
                  5 6       5
                                9
                                    4 5
                                          89
                                                             6 4 5
                                                             9 7
                                           3       3                                   3

      1 4 6     8 2 5               7      9       9                             7
                                           3       3 1       3       3                 3

      5 9 2         8               4
                                    7
                                               4
                                                       7         7               7
                                                                                       6




      8 3 7 6 2 5 9 4 1
                        1       3          3                 3 1   3 1         3

      2 7     5         4
                                9        8 9
                                                             6 4
                                                             9   8
                                                                         6
                                                                         9
                                                                               6
                                                                             8 9
          3                     3        2 3                       3   2       3
          6
          9   1 4
              5 6
              8
                    5
                      9 7 8 9
                                                                 5
                                                               7 8   7
                                                                         6   5 6
                                                                         9 7 8 9
          3 1     1   3   2 3                      3       2 3       1 2

          9
              5
              8   6 5
                      4
                      9 7 8 9                      9 7       9           7   9


      Back to Start                     Skip Animation


                                                           Helmut Simonis            Visualization Techniques   75
                                                          Introduction
                                          Visualization by Annotation
                                               Visualization Interface
                                                         Conclusions


Propagation Steps (Forward Checking)
              1 2                       2 3       3       2 3 1         1

      4         5 6
                            8           5
                                          9
                                                  6
                                                  9
                                                            6
                                                            9 7
                                                                5
                                                                        7
                                                                            6
                                                                            9 7
                                                                                5 6
                                                                                  9
          3       2             3                         2 3
          6
          9
                  5 6       5
                                9       1 7                 6 4 5
                                                            9   8
                                                                            6
                                                                            9
                                                                                    5 6
                                                                                    8 9
              1         1                                     1

  7
          6
          9         3 2
                  5 6       5
                                9
                                    4 5
                                          8
                                          9
                                                            6 4 5
                                                            9 7
                                          3       3                                   3

      1 4 6     8 2 5               7     9       9                             7
                                          3       3 1       3       3                 3

      5 9 2         8               4
                                    7
                                              4
                                                      7         7               7
                                                                                      6




      8 3 7 6 2 5 9 4 1
                        1       3         3                 3 1   3 1         3

      2 7     5         4
                                9       8 9
                                                            6
                                                            9   8       9   8 9
          3                     3       2 3                       3   2       3
          6
          9   1 4
              5 6
              8
                    5
                      9 7 8 9
                                                                5
                                                              7 8   7
                                                                            5
                                                                        9 7 8 9
          3 1     1   3   2 3                     3       2 3       1 2

          9
              5
              8   6 5
                      4
                      9 7 8 9                     9 7       9           7   9


      Back to Start


                                                          Helmut Simonis            Visualization Techniques   76
                                                          Introduction
                                          Visualization by Annotation
                                               Visualization Interface
                                                         Conclusions


After Setup (Forward Checking)
              1 2                       2 3       3       2 3 1         1

      4         5 6
                            8           5
                                          9
                                                  6
                                                  9
                                                            6
                                                            9 7
                                                                5
                                                                        7
                                                                            6
                                                                            9 7
                                                                                5 6
                                                                                  9
          3       2             3                         2 3
          6
          9
                  5 6       5
                                9       1 7                 6 4 5
                                                            9   8
                                                                            6
                                                                            9
                                                                                    5 6
                                                                                    8 9
              1         1                                     1

  7
          6
          9         3 2
                  5 6       5
                                9
                                    4 5
                                          8
                                          9
                                                            6 4 5
                                                            9 7
                                          3       3                                   3

      1 4 6     8 2 5               7     9       9                             7
                                          3       3 1       3       3                 3

      5 9 2         8               4
                                    7
                                              4
                                                      7         7               7
                                                                                      6




      8 3 7 6 2 5 9 4 1
                        1       3         3                 3 1   3 1         3

      2 7     5         4
                                9       8 9
                                                            6
                                                            9   8       9   8 9
          3                     3       2 3                       3   2       3
          6
          9   1 4
              5 6
              8
                    5
                      9 7 8 9
                                                                5
                                                              7 8   7
                                                                            5
                                                                        9 7 8 9
          3 1     1   3   2 3                     3       2 3       1 2

          9
              5
              8   6 5
                      4
                      9 7 8 9                     9 7       9           7   9




                                                          Helmut Simonis            Visualization Techniques   77
                                                           Introduction
                                           Visualization by Annotation
                                                Visualization Interface
                                                          Conclusions


Propagation Steps (Bounds Consistency)
               1   2   3               1 2 3 1 2 3 1   2   3   1   2   3   1   2   3   1   2   3

      4        4
               7
                   5
                   8
                       6
                       9       8       4 5 6 4 5 6 4
                                       7 8 9 7 8 9 7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2    3   1   2   3   1   2   3               1   2   3   1   2   3   1   2   3   1   2   3
  4
  7
      5
      8
           6
           9
               4
               7
                   5
                   8
                       6
                       9
                           4
                           7
                               5
                               8
                                   6
                                   9    1 7        4
                                                   7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2    3   1   2   3   1   2   3   1 2 3       1   2   3   1   2   3
  4
  7
      5
      8
           6
           9
               4
               7
                   5
                   8
                       6
                       9
                           4
                           7
                               5
                               8
                                   6
                                   9      8
                                       4 5 6
                                       7 8 9
                                                   4
                                                   7
                                                       5
                                                       8   3 2
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
  1   2    3   1   2   3               1 2 3 1 2 3                                     1   2   3
  4
  7
      5
      8
           6
           9
               4
               7
                   5
                   8
                       6
                       9       6       4 5 6 4 5 6
                                       7 8 9 7 8 9     8 2 5                           4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2    3               1 2 3       1 2 3 1 2 3 1   2   3   1 2 3                   1   2   3
  4
  7
      5
      8 9  6
           9
                           4 5 6
                           7 8 9
                                       4 5 6 4 5 6 4
                                       7 8 9 7 8 9 7
                                                       5
                                                       8   8
                                                           6
                                                           9
                                                               4 5 6
                                                               7 8 9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2    3                                 1 2 3 1   2   3               1   2   3   1   2   3
  4
  7
      5
      8 3 7 6
           6
           9
                                             4 5 6 4
                                             7 8 9 7
                                                       5
                                                       8 9 6
                                                           9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
                           1   2   3   1 2 3       1   2   3   1   2   3   1   2   3   1   2   3

      2 7     5            4
                           7
                               5
                               8
                                   6
                                   9
                                       4 5 6
                                       7 8 9
                                                   4
                                                   7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2    3   1   2   3   1   2   3   1 2 3                   1   2   3   1   2   3   1   2   3
  4
  7
      5
      8
           6
           9  1 4
               4
               7
                   5
                   8
                       6
                       9
                           4
                           7
                               5
                               8
                                   6
                                   9
                                       4 5 6
                                       7 8 9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2    3   1   2   3   1   2   3   1 2 3 1 2 3 1   2 3                 1   2   3
  4
  7
      5
      8
           6
           9
               4
               7
                   5
                   8
                       6
                       9
                           4
                           7
                               5
                               8
                                   6
                                   9
                                       4 5 6 4 5 6 4
                                       7 8 9 7 8 9 7
                                                       5 6
                                                       8 9         6       4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9       4
          Skip Animation


                                                       Helmut Simonis                      Visualization Techniques   78
                                                          Introduction
                                          Visualization by Annotation
                                               Visualization Interface
                                                         Conclusions


Propagation Steps (Bounds Consistency)
              1   2   3               1 2 3 1 2 3 1    2   3   1   2   3   1   2   3   1   2   3

      4       4
              7
                  5
                  8
                      6
                      9       8       4 5 6 4 5 6 4
                                      7 8 9 7 8 9 7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3   1   2   3   1   2   3               1    2   3   1   2   3   1   2   3   1   2   3
  4
  7
      5
      8
          6
          9
              4
              7
                  5
                  8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9    1 7        4
                                                  7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3   1   2   3   1   2   3   1 2 3       1    2   3   1   2   3
  4
  7
      5
      8
          6
          9
              4
              7
                  5
                  8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9      8
                                      4 5 6
                                      7 8 9
                                                  4
                                                  7
                                                       5
                                                       8  3 2
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
  1   2   3   1   2   3               1 2 3 1 2 3                                      1   2   3
  4
  7
      5
      8
          6
          9
              4
              7
                  5
                  8
                      6
                      9       6       4 5 6 4 5 6
                                      7 8 9 7 8 9     8 2 5                            4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3               1 2 3       1 2 3 1 2 3 1    2   3   1 2 3                   1   2   3
  4
  7
      5
      8 9 6
          9
                          4 5 6
                          7 8 9
                                      4 5 6 4 5 6 4
                                      7 8 9 7 8 9 7
                                                       5
                                                       8  86
                                                           9
                                                               4 5 6
                                                               7 8 9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3                                 1 2 3 1    2   3               1   2   3   1   2   3
  4
  7
      5
      8 3 7 6
          6
          9
                                            4 5 6 4
                                            7 8 9 7
                                                       5
                                                       89  6
                                                           9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
                          1   2   3   1 2 3       1    2   3   1   2   3   1   2   3   1   2   3

      2 7     5           4
                          7
                              5
                              8
                                  6
                                  9
                                      4 5 6
                                      7 8 9
                                                  4
                                                  7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3   1   2   3   1   2   3   1 2 3                    1   2   3   1   2   3   1   2   3
  4
  7
      5
      8
          6
          9   1 4
              4
              7
                  5
                  8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9
                                      4 5 6
                                      7 8 9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3   1   2   3   1   2   3   1 2 3 1 2 3 1    2 3                 1   2   3
  4
  7
      5
      8
          6
          9
              4
              7
                  5
                  8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9
                                      4 5 6 4 5 6 4
                                      7 8 9 7 8 9 7
                                                       5 6
                                                       8 9         6       4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9       4
      Back to Start                   Skip Animation


                                                       Helmut Simonis                      Visualization Techniques   79
                                                          Introduction
                                          Visualization by Annotation
                                               Visualization Interface
                                                         Conclusions


Propagation Steps (Bounds Consistency)
              1 2     3               1 2 3 1 2 3 1    2 3     1 2     3   1 2     3   1 2     3

      4       7
                5     6
                      9       8       7
                                        5 6
                                          9 7
                                              5 6
                                                9 7
                                                       5 6
                                                         9     7
                                                                 5     6
                                                                       9   7
                                                                             5     6
                                                                                   9   7
                                                                                         5     6
                                                                                               9
  1   2   3   1 2     3   1   2   3               1    2 3     1 2     3   1 2     3   1 2     3
  4
  7
      5
      8
          6
          9
              4 5
              7 8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9    1 7        4
                                                  7
                                                       5 6
                                                       8 9
                                                               4 5
                                                               7 8
                                                                       6
                                                                       9
                                                                           4 5
                                                                           7 8
                                                                                   6
                                                                                   9
                                                                                       4 5
                                                                                       7 8
                                                                                               6
                                                                                               9
  1   2   3   1 2     3   1   2   3   1 2 3       1    2 3     1 2     3
  4
  7
      5
      8
          6
          9
              4 5
              7 8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9      8
                                      4 5 6
                                      7 8 9
                                                  4
                                                  7
                                                       5 6
                                                       8 93 2  4 5
                                                               7 8
                                                                       6
                                                                       9
  1   2   3   1 2     3               1 2 3 1 2 3                                      1   2   3
  4
  7
      5
      8
          6
          9
              4 5
              7 8
                      6
                      9       6       4 5 6 4 5 6
                                      7 8 9 7 8 9     8 2 5                            4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3               1 2 3       1 2 3 1 2 3 1    2   3   1 2 3                   1   2   3
  4
  7
      5
      8 9 6
          9
                          4 5 6
                          7 8 9
                                      4 5 6 4 5 6 4
                                      7 8 9 7 8 9 7
                                                       5
                                                       8  86
                                                           9
                                                               4 5 6
                                                               7 8 9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3                                 1 2 3 1    2   3               1   2   3   1   2   3
  4
  7
      5
      8 3 7 6
          6
          9
                                            4 5 6 4
                                            7 8 9 7
                                                       5
                                                       89  6
                                                           9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
                          1   2   3   1 2 3       1    2   3   1   2   3   1   2   3   1   2   3

      2 7     5           4
                          7
                              5
                              8
                                  6
                                  9
                                      4 5 6
                                      7 8 9
                                                  4
                                                  7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3   1   2   3   1   2   3   1 2 3                    1   2   3   1   2   3   1   2   3
  4
  7
      5
      8
          6
          9   1 4
              4
              7
                  5
                  8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9
                                      4 5 6
                                      7 8 9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3   1   2   3   1   2   3   1 2 3 1 2 3 1    2 3                 1   2   3
  4
  7
      5
      8
          6
          9
              4
              7
                  5
                  8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9
                                      4 5 6 4 5 6 4
                                      7 8 9 7 8 9 7
                                                       5 6
                                                       8 9         6       4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9       4
      Back to Start                   Skip Animation


                                                       Helmut Simonis                      Visualization Techniques   80
                                                      Introduction
                                      Visualization by Annotation
                                           Visualization Interface
                                                     Conclusions


Propagation Steps (Bounds Consistency)
          1 2     3               1 2 3 1 2 3 1    2 3     1 2     3   1 2     3   1 2     3

      4   7
            5     6
                  9       8       7
                                    5 6
                                      9 7
                                          5 6
                                            9 7
                                                   5 6
                                                     9     7
                                                             5     6
                                                                   9   7
                                                                         5     6
                                                                               9   7
                                                                                     5     6
                                                                                           9
  1   3   1 2     3   1   2   3               1    2 3     1 2     3   1 2     3   1 2     3
    5 6
  7 8 9
          4 5
          7 8
                  6
                  9
                      4
                      7
                          5
                          8
                              6
                              9    1 7        4
                                              7
                                                   5 6
                                                   8 9
                                                           4 5
                                                           7 8
                                                                   6
                                                                   9
                                                                       4 5
                                                                       7 8
                                                                               6
                                                                               9
                                                                                   4 5
                                                                                   7 8
                                                                                           6
                                                                                           9
  1   3   1 2     3   1   2   3   1 2 3       1    2 3     1 2     3
    5 6
  7 8 9
          4 5
          7 8
                  6
                  9
                      4
                      7
                          5
                          8
                              6
                              9      8
                                  4 5 6
                                  7 8 9
                                              4
                                              7
                                                   5 6
                                                   8 93 2  4 5
                                                           7 8
                                                                   6
                                                                   9
  1   3   1 2     3               1 2 3 1 2 3                                      1   2   3
    5 6
  7 8 9
          4 5
          7 8
                  6
                  9       6       4 5 6 4 5 6
                                  7 8 9 7 8 9     8 2 5                            4
                                                                                   7
                                                                                       5
                                                                                       8
                                                                                           6
                                                                                           9
  1   3               1 2 3       1 2 3 1 2 3 1    2   3   1 2 3                   1   2   3
    5 6
  7 8 9 9             4 5 6
                      7 8 9
                                  4 5 6 4 5 6 4
                                  7 8 9 7 8 9 7
                                                   5
                                                   8  86
                                                       9
                                                           4 5 6
                                                           7 8 9
                                                                                   4
                                                                                   7
                                                                                       5
                                                                                       8
                                                                                           6
                                                                                           9
  1   3                                 1 2 3 1    2   3               1   2   3   1   2   3
    5 6
  7 8 9 3 7 6                           4 5 6 4
                                        7 8 9 7
                                                   5
                                                   89  6
                                                       9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
                                                                                   4
                                                                                   7
                                                                                       5
                                                                                       8
                                                                                           6
                                                                                           9
                      1   2   3   1 2 3       1    2   3   1   2   3   1   2   3   1   2   3

      2 7     5       4
                      7
                          5
                          8
                              6
                              9
                                  4 5 6
                                  7 8 9
                                              4
                                              7
                                                   5
                                                   8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
                                                                                   4
                                                                                   7
                                                                                       5
                                                                                       8
                                                                                           6
                                                                                           9
  1   3   1   2   3   1   2   3   1 2 3                    1   2   3   1   2   3   1   2   3
    5 6
  7 8 9
          4
          7   1 4
              5
              8
                  6
                  9
                      4
                      7
                          5
                          8
                              6
                              9
                                  4 5 6
                                  7 8 9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
                                                                                   4
                                                                                   7
                                                                                       5
                                                                                       8
                                                                                           6
                                                                                           9
  1   3   1   2   3   1   2   3   1 2 3 1 2 3 1    2 3                 1   2   3
    5 6
  7 8 9
          4
          7
              5
              8
                  6
                  9
                      4
                      7
                          5
                          8
                              6
                              9
                                  4 5 6 4 5 6 4
                                  7 8 9 7 8 9 7
                                                   5 6
                                                   8 9         6       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9       4
      Back to Start               Skip Animation


                                                   Helmut Simonis                      Visualization Techniques   81
                                                        Introduction
                                        Visualization by Annotation
                                             Visualization Interface
                                                       Conclusions


Propagation Steps (Bounds Consistency)
            1 2     3               1 2 3 1 2 3 1 2 3 1    2 3 1 2 3 1 2   3

      4     7
              5     6
                    9       8       7
                                      5 6
                                        9 7
                                            5 6
                                              9 7
                                                  5 6
                                                    9 7
                                                           5 6
                                                             9 7
                                                                 5 6
                                                                   9 7
                                                                       5   6
                                                                           9
        3     2     3     2     3                 2 3      2 3   2 3   2   3
      5 6
      8 9
            4 5
              8
                    6
                    9
                        4 5
                          8
                                6
                                9    1 7        4 5 6 4
                                                  8 9
                                                           5 6 4 5 6 4 5
                                                           8 9   8 9   8
                                                                           6
                                                                           9
  1     3   1 2     3   1 2     3   1 2 3       1 2 3 1    2 3

  7
      5 6
      8 9
            4 5
            7 8
                    6
                    9
                        4 5
                        7 8
                                6
                                9      8
                                    4 5 6
                                    7 8 9             3 2
                                                4 5 6 4
                                                7 8 9 7
                                                           5 6
                                                           8 9
  1     3   1 2     3               1 2 3 1 2 3                      1 2   3

  7
      5 6
      8 9
            4 5
            7 8
                    6
                    9       6       4 5 6 4 5 6
                                    7 8 9 7 8 9   8 2 5              4 5
                                                                     7 8
                                                                           6
                                                                           9
  1     3               1 2 3       1 2 3 1 2 3 1 2 3 1    2 3       1 2   3

  7     9
      5 6
      8 9
                        4 5 6
                        7 8 9                         8
                                    4 5 6 4 5 6 4 5 6 4
                                    7 8 9 7 8 9 7 8 9 7
                                                           5 6
                                                           8 9
                                                                     4 5
                                                                     7 8
                                                                           6
                                                                           9
  1     3                                 1 2 3 1 2 3          1 2 3 1 2   3

  7     3 7 6
      5 6
      8 9                                           9
                                          4 5 6 4 5 6
                                          7 8 9 7 8 9
                                                               4 5 6 4 5
                                                               7 8 9 7 8
                                                                           6
                                                                           9
                        1   2   3   1 2 3       1 2 3 1    2 3 1 2 3 1 2   3

      2 7     5         4
                        7
                            5
                            8
                                6
                                9
                                    4 5 6
                                    7 8 9
                                                4 5 6 4
                                                7 8 9 7
                                                           5 6 4 5 6 4 5
                                                           8 9 7 8 9 7 8
                                                                           6
                                                                           9
  1   3     1   2   3   1   2   3   1 2 3             1    2 3 1 2 3 1 2   3
    5 6
  7 8 9
            4
            7 1 4
                5
                8
                    6
                    9
                        4
                        7
                            5
                            8
                                6
                                9
                                    4 5 6
                                    7 8 9
                                                      4
                                                      7
                                                           5 6 4 5 6 4 5
                                                           8 9 7 8 9 7 8
                                                                           6
                                                                           9
  1   3     1   2   3   1   2   3   1 2 3 1 2 3 1 2 3          1 2 3
    5 6
  7 8 9
            4
            7
                5
                8
                    6
                    9
                        4
                        7
                            5
                            8
                                6
                                9
                                    4 5 6 4 5 6 4 5 6
                                    7 8 9 7 8 9 7 8 9     6    4 5 6
                                                               7 8 9   4
      Back to Start                 Skip Animation


                                                     Helmut Simonis    Visualization Techniques   82
                                                  Introduction
                                  Visualization by Annotation
                                       Visualization Interface
                                                 Conclusions


Propagation Steps (Bounds Consistency)
            1 2               1 2 3 1 2 3 1 2 3 1    2 3 1 2 3 1 2   3

      4       5 6
                    8         7
                                5 6
                                  9 7
                                      5 6
                                        9 7
                                            5 6
                                              9 7
                                                     5 6
                                                       9 7
                                                           5 6
                                                             9 7
                                                                 5   6
                                                                     9
        3     2     2 3                     2 3      2 3   2 3   2   3
      5 6
      8 9
            4 5 6 4 5 6
              8     8 9        1 7        4 5 6 4
                                            8 9
                                                     5 6 4 5 6 4 5
                                                     8 9   8 9   8
                                                                     6
                                                                     9
  1     3   1 2   1 2 3       1 2 3       1 2 3 1    2 3

  7
      5 6
      8 9
            4 5 6 4 5 6
              8   7 8 9          8
                              4 5 6
                              7 8 9             3 2
                                          4 5 6 4
                                          7 8 9 7
                                                     5 6
                                                     8 9
  1     3   1 2               1 2 3 1 2 3                      1 2   3

  7
      5 6
      8 9
            4 5 6
              8     6         4 5 6 4 5 6
                              7 8 9 7 8 9   8 2 5              4 5
                                                               7 8
                                                                     6
                                                                     9
  1     3         1 2 3       1 2 3 1 2 3 1 2 3 1    2 3       1 2   3

  7     9
      5 6
      8 9
                  4 5 6
                  7 8 9                         8
                              4 5 6 4 5 6 4 5 6 4
                              7 8 9 7 8 9 7 8 9 7
                                                     5 6
                                                     8 9
                                                               4 5
                                                               7 8
                                                                     6
                                                                     9
  1     3                           1 2 3 1 2 3          1 2 3 1 2   3

  7     3 7 6
      5 6
      8 9                                     9
                                    4 5 6 4 5 6
                                    7 8 9 7 8 9
                                                         4 5 6 4 5
                                                         7 8 9 7 8
                                                                     6
                                                                     9
                1     2   3   1 2 3       1 2 3 1    2 3 1 2 3 1 2   3

      2 7     5 4
                7
                      5
                      8
                          6
                          9
                              4 5 6
                              7 8 9
                                          4 5 6 4
                                          7 8 9 7
                                                     5 6 4 5 6 4 5
                                                     8 9 7 8 9 7 8
                                                                     6
                                                                     9
  1     3 1 2   1     2   3   1 2 3             1    2 3 1 2 3 1 2   3

  7   8 9   8 1 4
      5 6 4 5 6 4
                7
                      5
                      8
                          6
                          9
                              4 5 6
                              7 8 9
                                                4
                                                7
                                                     5 6 4 5 6 4 5
                                                     8 9 7 8 9 7 8
                                                                     6
                                                                     9
  1     3 1 2   1     2   3   1 2 3 1 2 3 1 2 3          1 2 3

  7
      5 6 4 5 6 4
      8 9   8   7
                      5
                      8
                          6
                          9
                              4 5 6 4 5 6 4 5 6
                              7 8 9 7 8 9 7 8 9     6    4 5 6
                                                         7 8 9   4
      Back to Start           Skip Animation


                                               Helmut Simonis    Visualization Techniques   83
                                            Introduction
                            Visualization by Annotation
                                 Visualization Interface
                                           Conclusions


Propagation Steps (Bounds Consistency)
          1 2           1 2 3 1 2 3 1 2 3 1    2 3 1 2 3 1 2               3

      4     5 6
                  8     7
                          5 6
                            9 7
                                5 6
                                  9 7
                                      5 6
                                        9 7
                                               5 6
                                                 9 7
                                                     5 6
                                                       9 7
                                                           5               6
                                                                           9
        3   2     2 3                 2 3      2 3   2 3   2               3
      5 6 4 5 6 4 5 6
      8 9   8     8 9    1 7        4 5 6 4
                                      8 9
                                               5 6 4 5 6 4 5
                                               8 9   8 9   8
                                                                           6
                                                                           9
  1       1     1       1           1     1

  7
      5 6 4 5 6 4 5 6
        9       7   9   7  8
                        4 5 6
                            9
                                    4 5 6 4
                                    7     3 2
                                        9 7
                                               5 6
                                                 9
  1     3 1 2           1 2 3 1 2 3                                1   2   3

  7
      5 6 4 5 6
      8 9   8     6     4 5 6 4 5 6
                        7 8 9 7 8 9   8 2 5                        4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3       1 2 3   1 2 3 1 2 3 1 2 3 1    2 3                 1   2   3

  7     9
      5 6
      8 9
                4 5 6
                7 8 9                     8
                        4 5 6 4 5 6 4 5 6 4
                        7 8 9 7 8 9 7 8 9 7
                                               5 6
                                               8 9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3                     1 2 3 1 2 3              1   2   3   1   2   3

  7     3 7 6
      5 6
      8 9                               9
                              4 5 6 4 5 6
                              7 8 9 7 8 9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
                1 2 3   1 2 3       1 2 3 1    2   3   1   2   3   1   2   3

      2 7     5 4 5 6
                7 8 9
                        4 5 6
                        7 8 9
                                    4 5 6 4
                                    7 8 9 7
                                               5
                                               8
                                                   6
                                                   9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3   1 2 3             1    2   3   1   2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5 6
                7 8 9
                        4 5 6
                        7 8 9
                                          4
                                          7
                                               5
                                               8
                                                   6
                                                   9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3   1 2 3 1 2 3 1 2 3              1   2   3

  7
      5 6 4 5 6 4 5 6
      8 9   8   7 8 9
                        4 5 6 4 5 6 4 5 6
                        7 8 9 7 8 9 7 8 9     6        4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9       4
      Back to Start     Skip Animation


                                         Helmut Simonis                Visualization Techniques   84
                                            Introduction
                            Visualization by Annotation
                                 Visualization Interface
                                           Conclusions


Propagation Steps (Bounds Consistency)
          1 2           1 2 3 1 2 3 1 2 3 1    2 3 1 2 3 1 2               3

      4     5 6
                  8     7
                          5 6
                            9 7
                                5 6
                                  9 7
                                      5 6
                                        9 7
                                               5 6
                                                 9 7
                                                     5 6
                                                       9 7
                                                           5               6
                                                                           9
        3   2     2 3                 2 3      2 3   2 3   2               3
      5 6 4 5 6 4 5
      8 9   8       9    1 7        4 5 6 4
                                      8 9
                                               5 6 4 5 6 4 5
                                               8 9   8 9   8
                                                                           6
                                                                           9
  1       1     1       1           1     1

  7
      5 6 4 5 6 4 5
        9           9   7  8
                        4 5 6
                            9
                                    4 5 6 4
                                    7     3 2
                                        9 7
                                               5 6
                                                 9
  1     3 1 2           1 2 3 1 2 3                                1   2   3

  7
      5 6 4 5 6
      8 9   8     6     4 5 6 4 5 6
                        7 8 9 7 8 9   8 2 5                        4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3       1 2 3   1 2 3 1 2 3 1 2 3 1    2 3                 1   2   3

  7     9
      5 6
      8 9
                4 5
                    9                     8
                        4 5 6 4 5 6 4 5 6 4
                        7 8 9 7 8 9 7 8 9 7
                                               5 6
                                               8 9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3                     1 2 3 1 2 3              1   2   3   1   2   3

  7     3 7 6
      5 6
      8 9                               9
                              4 5 6 4 5 6
                              7 8 9 7 8 9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
                1 2 3   1 2 3       1 2 3 1    2   3   1   2   3   1   2   3

      2 7     5 4 5
                    9
                        4 5 6
                        7 8 9
                                    4 5 6 4
                                    7 8 9 7
                                               5
                                               8
                                                   6
                                                   9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3   1 2 3             1    2   3   1   2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5
                    9
                        4 5 6
                        7 8 9
                                          4
                                          7
                                               5
                                               8
                                                   6
                                                   9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3   1 2 3 1 2 3 1 2 3              1   2   3

  7
      5 6 4 5 6 4 5
      8 9   8       9
                        4 5 6 4 5 6 4 5 6
                        7 8 9 7 8 9 7 8 9     6        4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9       4
      Back to Start     Skip Animation


                                         Helmut Simonis                Visualization Techniques   85
                                            Introduction
                            Visualization by Annotation
                                 Visualization Interface
                                           Conclusions


Propagation Steps (Bounds Consistency)
          1 2           1 2 3 1 2 3 1 2 3 1    2 3 1 2 3 1 2               3

      4     5 6
                  8     7
                          5 6
                            9 7
                                5 6
                                  9 7
                                      5 6
                                        9 7
                                               5 6
                                                 9 7
                                                     5 6
                                                       9 7
                                                           5               6
                                                                           9
        3   2     2 3                 2 3      2 3   2 3   2               3
      5 6 4 5 6 4 5
      8 9   8       9    1 7        4 5 6 4
                                      8 9
                                               5 6 4 5 6 4 5
                                               8 9   8 9   8
                                                                           6
                                                                           9
  1       1     1       1           1     1

  7
      5 6 4 5 6 4 5
        9           9   7  8
                        4 5 6
                            9
                                    4 5 6 4
                                    7     3 2
                                        9 7
                                               5 6
                                                 9
  1     3 1             1   3 1   3                                1       3

  7     9
          4
                  6     4
                        7
                              4
                            9 7   9   8 2 5                        4
                                                                   7       9
  1     3       1 2 3   1 2 3 1 2 3 1 2 3 1    2 3                 1   2   3

  7     9
      5 6
      8 9
                4 5
                    9                     8
                        4 5 6 4 5 6 4 5 6 4
                        7 8 9 7 8 9 7 8 9 7
                                               5 6
                                               8 9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3                     1 2 3 1 2 3              1   2   3   1   2   3

  7     3 7 6
      5 6
      8 9                               9
                              4 5 6 4 5 6
                              7 8 9 7 8 9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
                1 2 3   1 2 3       1 2 3 1    2   3   1   2   3   1   2   3

      2 7     5 4 5
                    9
                        4 5 6
                        7 8 9
                                    4 5 6 4
                                    7 8 9 7
                                               5
                                               8
                                                   6
                                                   9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3   1 2 3             1    2   3   1   2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5
                    9
                        4 5 6
                        7 8 9
                                          4
                                          7
                                               5
                                               8
                                                   6
                                                   9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3   1 2 3 1 2 3 1 2 3              1   2   3

  7
      5 6 4 5 6 4 5
      8 9   8       9
                        4 5 6 4 5 6 4 5 6
                        7 8 9 7 8 9 7 8 9     6        4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9       4
      Back to Start     Skip Animation


                                         Helmut Simonis                Visualization Techniques   86
                                              Introduction
                              Visualization by Annotation
                                   Visualization Interface
                                             Conclusions


Propagation Steps (Bounds Consistency)
          1 2              2 3 1 2 3 1 2 3     1 2     3 1 2 3 1 2             3

      4     5 6
                  8   7
                           5
                             9 7
                                 5 6
                                   9 7
                                       5 6
                                         9     7
                                                 5     6
                                                       9 7
                                                           5 6
                                                             9 7
                                                                 5             6
                                                                               9
        3   2     2 3                  2 3       2     3   2 3   2             3
      5 6 4 5 6 4 5
      8 9   8       9     1 7        4 5 6
                                       8 9
                                               4 5
                                                 8
                                                       6 4 5 6 4 5
                                                       9   8 9   8
                                                                               6
                                                                               9
  1       1     1                    1         1

  7
      5 6 4 5 6 4 5
        9
                      4
                    9 7
                           5
                            89
                                     4 5 6
                                     7   9  3 24 5
                                               7
                                                       6
                                                       9
  1     3 1                  3 1   3                                   1       3

  7     9
          4
                  6   4
                      7
                               4
                             9 7   9    8 2 5                          4
                                                                       7       9
  1     3       1 2 3      2 3 1 2 3 1 2 3     1 2 3                   1   2   3

  7     9
      5 6
      8 9
                4 5   4
                    9 7
                           5   4 5 6 4 5 6
                           8 9 7 8 9 7 8 9  8  4 5 6
                                               7 8 9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3                      1 2 3 1 2 3                 1   2   3   1   2   3

  7     3 7 6
      5 6
      8 9
                               4 5 6 4 5 6
                               7 8 9 7 8 99                4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
                1 2 3      2 3       1 2 3     1   2   3   1   2   3   1   2   3

      2 7     5 4 5   4
                    9 7
                           5
                           8 9
                                     4 5 6
                                     7 8 9
                                               4
                                               7
                                                   5
                                                   8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3      2 3                 1   2   3   1   2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5   4
                    9 7
                           5
                           8 9
                                               4
                                               7
                                                   5
                                                   8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3      2 3 1 2 3 1 2 3                 1   2   3

  7
      5 6 4 5 6 4 5
      8 9   8
                      4
                    9 7
                           5   4 5 6 4 5 6
                           8 9 7 8 9 7 8 9         6       4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9       4
      Back to Start       Skip Animation


                                           Helmut Simonis                  Visualization Techniques   87
                                              Introduction
                              Visualization by Annotation
                                   Visualization Interface
                                             Conclusions


Propagation Steps (Bounds Consistency)
          1 2              2 3 1 2 3 1 2 3     1 2     3 1 2 3 1 2             3

      4     5 6
                  8   7
                           5
                             9 7
                                 5 6
                                   9 7
                                       5 6
                                         9     7
                                                 5     6
                                                       9 7
                                                           5 6
                                                             9 7
                                                                 5             6
                                                                               9
        3   2     2 3                  2 3       2     3   2 3   2             3
      5 6 4 5 6 4 5
      8 9   8       9     1 7        4 5 6
                                       8 9
                                               4 5
                                                 8
                                                       6 4 5 6 4 5
                                                       9   8 9   8
                                                                               6
                                                                               9
  1       1     1                    1         1

  7
      5 6 4 5 6 4 5
        9
                      4
                    9 7
                           5
                            89
                                     4 5 6
                                     7   9  3 24 5
                                               7
                                                       6
                                                       9
  1     3 1                  3 1   3                                   1       3

  7     9
          4
                  6   4
                      7
                               4
                             9 7   9    8 2 5                          4
                                                                       7     9
  1     3       1 2 3      2 3 1 2 3 1 2 3     1 2 3                   1   2 3

  7     9
      5 6       4 5   4
                      7
                           5   4 5 6 4 5 6
                               7     7      8  4 5 6
                                               7
                                                                       4
                                                                       7
                                                                           5 6

  1     3                      1 2 3 1 2 3                 1   2   3   1   2   3

  7     3 7 6
      5 6
      8 9
                               4 5 6 4 5 6
                               7 8 9 7 8 99                4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
                1 2 3      2 3       1 2 3     1   2   3   1   2   3   1   2   3

      2 7     5 4 5   4
                    9 7
                           5
                           8 9
                                     4 5 6
                                     7 8 9
                                               4
                                               7
                                                   5
                                                   8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3      2 3                 1   2   3   1   2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5   4
                    9 7
                           5
                           8 9
                                               4
                                               7
                                                   5
                                                   8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3      2 3 1 2 3 1 2 3                 1   2   3

  7
      5 6 4 5 6 4 5
      8 9   8
                      4
                    9 7
                           5   4 5 6 4 5 6
                           8 9 7 8 9 7 8 9         6       4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9       4
      Back to Start       Skip Animation


                                           Helmut Simonis                  Visualization Techniques   88
                                              Introduction
                              Visualization by Annotation
                                   Visualization Interface
                                             Conclusions


Propagation Steps (Bounds Consistency)
          1 2              2 3       2 3 1 2 3   1 2   3 1 2 3 1 2             3

      4     5 6
                  8   7
                           5
                             9
                                       6
                                       9 7
                                           5 6
                                             9   7
                                                   5   6
                                                       9 7
                                                           5 6
                                                             9 7
                                                                 5             6
                                                                               9
        3   2     2 3                      2 3     2   3   2 3   2             3
      5 6 4 5 6 4 5
      8 9   8       9     1 7            4 5 6
                                           8 9
                                                 4 5
                                                   8
                                                       6 4 5 6 4 5
                                                       9   8 9   8
                                                                               6
                                                                               9
  1       1     1                        1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7     89
                                         4 5 6
                                         7   93 24 5
                                                 7
                                                       6
                                                       9
  1     3 1                  3         3                               1       3

  7     9
          4
                  6   4
                      7      9
                                 4
                                   9      8 2 5                        4
                                                                       7     9
  1     3       1 2 3   2    3   2 3 1 2 3 1 2         3               1   2 3

  7     9
      5 6       4 5   4 5
                      7
                               4   6 4 5
                                     7
                                         6 4 5
                                           7  8        6               4
                                                                       7
                                                                           5 6

  1     3                        2 3 1 2 3                 1   2   3   1   2   3

  7     3 7 6
      5 6
      8 9
                               4   6 4 5
                                   9 7 8
                                         6
                                         9  9              4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
                1 2 3   2    3       1 2 3 1 2         3   1   2   3   1   2   3

      2 7     5 4 5   4 5
                    9 7 8    9
                                     4 5
                                     7 8
                                         6 4 5
                                         9 7 8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3   2    3             1 2         3   1   2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5   4 5
                    9 7 8    9
                                           4 5
                                           7 8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3   2    3   2 3 1 2 3                 1   2   3

  7
      5 6 4 5 6 4 5
      8 9   8
                      4 5
                    9 7 8    9
                               4   6 4 5 6
                                   9 7 8 9        6        4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9       4
      Back to Start       Skip Animation


                                           Helmut Simonis                  Visualization Techniques   89
                                                Introduction
                                Visualization by Annotation
                                     Visualization Interface
                                               Conclusions


Propagation Steps (Bounds Consistency)
          1 2                2 3       2 3 1 2 3   1 2   3 1 2 3 1 2           3

      4     5 6
                  8     7
                             5
                               9
                                         6
                                         9 7
                                             5 6
                                               9   7
                                                     5   6
                                                         9 7
                                                             5 6
                                                               9 7
                                                                   5           6
                                                                               9
        3   2     2 3                        2 3     2   3   2 3   2           3
      5 6 4 5 6 4 5
      8 9   8       9       1 7            4 5 6
                                             8 9
                                                   4 5
                                                     8
                                                         6 4 5 6 4 5
                                                         9   8 9   8
                                                                               6
                                                                               9
  1       1     1                          1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7       89
                                           4 5 6
                                           7   93 24 5
                                                   7
                                                         6
                                                         9
  1     3 1                    3         3                             1       3

  7     9
          4
                  6   4
                      7        9  9
                                   4
                                            8 2 5                      4
                                                                       7     9
  1     3       1 2 3   2      32 3 1 2        3 1 2 3                 1   2 3

  7     9
      5 6       4 5   4 5
                      7
                              4   6 4 5
                                    7           8
                                               6 4 5 6
                                                 7
                                                                       4
                                                                       7
                                                                           5 6

  1                             2   1 2                      1 2       1   2
      5
      8 3 7 6                 4     4 5
                                      8       9              4 5
                                                               8
                                                                       4   5
                                                                           8
                1 2 3     2 3       1 2        3 1 2 3       1 2   3   1   2   3

      2 7     5 4 5
                    9
                        4 5
                        7 8 9
                                    4 5
                                    7 8
                                               6 4 5 6
                                               9 7 8 9
                                                             4 5
                                                             7 8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3     2 3                    1 2 3       1 2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5
                    9
                        4 5
                        7 8 9
                                                 4 5 6
                                                 7 8 9
                                                             4 5
                                                             7 8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3     2 3   2 3 1 2        3             1 2   3

  7
      5 6 4 5 6 4 5
      8 9   8       9
                        4 5
                        7 8 9
                              4   6 4 5
                                  9 7 8
                                               6
                                               9    6        4 5
                                                             7 8
                                                                   6
                                                                   9       4
      Back to Start         Skip Animation


                                             Helmut Simonis                Visualization Techniques   90
                                               Introduction
                               Visualization by Annotation
                                    Visualization Interface
                                              Conclusions


Propagation Steps (Bounds Consistency)
          1 2              2 3         2 3 1 2 3   1 2   3 1 2 3 1 2       3

      4     5 6
                  8   7
                           5
                             9
                                         6
                                         9 7
                                             5 6
                                               9   7
                                                     5   6
                                                         9 7
                                                             5 6
                                                               9 7
                                                                   5       6
                                                                           9
        3   2     2 3                        2 3     2   3   2 3   2       3
      5 6 4 5 6 4 5
      8 9   8       9     1 7                5 6
                                               9
                                                   4 5
                                                     8
                                                         6 4 5 6 4 5
                                                         9   8 9   8
                                                                           6
                                                                           9
  1       1     1                          1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7     8  9           7
                                             5 6
                                               93 24 5
                                                   7
                                                         6
                                                         9
  1     3 1                    3         3                         1       3

  7     9
          4
                  6   4
                      7        9
                                   4
                                       9    8 2 5                  4
                                                                   7     9
  1     3       1 2 3   2      3     2 3 1 2 3 1 2 3               1   2 3

  7     9
      5 6       4 5   4 5
                      7
                                   4   6
                                         7      8
                                           5 6 4 5 6
                                               7
                                                                   4
                                                                   7
                                                                       5 6

  1                                  2   1 2         1 2           1   2
      5
      8 3 7 6                      4       5
                                              9      4 5
                                                       8
                                                                   4   5
                                                                       8
                1 2 3      2   3         1 2 3 1 2 3 1 2       3   1   2   3

      2 7     5 4 5   4
                    9 7
                           5
                           8   9         7
                                           5 6 4 5 6 4 5
                                             9 7 8 9 7 8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3      2   3               1 2 3 1 2       3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5   4
                    9 7
                           5
                           8   9
                                               4 5 6 4 5
                                               7 8 9 7 8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3      2   3     2 3 1 2 3       1 2       3

  7
      5 6 4 5 6 4 5
      8 9   8
                      4
                    9 7
                           5
                           8   9
                                   4   6
                                       9 7
                                           5 6
                                             9      64 5
                                                     7 8
                                                               6
                                                               9       4
      Back to Start       Skip Animation


                                             Helmut Simonis            Visualization Techniques   91
                                                       Introduction
                                       Visualization by Annotation
                                            Visualization Interface
                                                      Conclusions


Propagation Steps (Bounds Consistency)
          1 2                      2 3         2 3 1 2 3   1 2   3 1 2 3 1 2       3

      4     5 6
                      8       7
                                   5
                                     9
                                                 6
                                                 9 7
                                                     5 6
                                                       9   7
                                                             5   6
                                                                 9 7
                                                                     5 6
                                                                       9 7
                                                                           5       6
                                                                                   9
        3   2     2 3                                2 3     2   3   2 3   2       3
      5 6 4 5 6 4 5
      8 9   8       9             1 7                5 6
                                                       9
                                                           4 5
                                                             8
                                                                 6 4 5 6 4 5
                                                                 9   8 9   8
                                                                                   6
                                                                                   9
  1       1     1                                  1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7             8  9           7
                                                     5 6
                                                       93 24 5
                                                           7
                                                                 6
                                                                 9
  1     3 1                            3         3                         1       3

  7     9
          4
                      6
                      4
                      7                9
                                           4
                                               9    8 2 5                  4
                                                                           7     9
  1     3       1 2 3   2              3     2 3 1 2 3 1 2 3               1   2 3

  7     9
      5 6       4 5   4 5
                      7
                                           4   6
                                                 7      8
                                                   5 6 4 5 6
                                                       7
                                                                           4
                                                                           7
                                                                               5 6

  1                                          2   1 2         1 2           1   2
      5
      8 3 7 6                              4       5
                                                      9      4 5
                                                               8
                                                                           4   5
                                                                               8
                  1       3            3         1   3 1   3 1         3   1       3

      2 7     5   4
                        9
                              4
                                   8   9
                                                     6 4
                                                     9
                                                           6 4
                                                         8 9   8
                                                                       6
                                                                       9
                                                                           4
                                                                             8
                                                                                   6
                                                                                   9
  1   3   1 2     1   2 3          2   3               1 2 3 1 2       3   1 2     3
    5 6
  7 8 9     8 1 4
          4 5 6   4   5
                        9
                              4
                              7
                                   5
                                   8   9
                                                       4 5 6 4 5
                                                       7 8 9 7 8
                                                                       6
                                                                       9
                                                                           4 5
                                                                           7 8
                                                                                   6
                                                                                   9
  1   3   1 2     1   2 3          2   3     2 3 1 2 3       1 2       3
    5 6
  7 8 9
          4 5 6
            8
                  4   5
                        9
                              4
                              7
                                   5
                                   8   9
                                           4   6
                                               9 7
                                                   5 6
                                                     9      64 5
                                                             7 8
                                                                       6
                                                                       9       4
      Back to Start               Skip Animation


                                                     Helmut Simonis            Visualization Techniques   92
                                                       Introduction
                                       Visualization by Annotation
                                            Visualization Interface
                                                      Conclusions


Propagation Steps (Bounds Consistency)
          1 2                      2 3         2 3 1 2 3   1   3 1 2   3 1 2 3

      4     5 6
                      8       7
                                   5
                                     9
                                                 6
                                                 9 7
                                                     5 6
                                                       9   7
                                                               5
                                                                 7
                                                                   5   6
                                                                       9 7
                                                                           5 6
                                                                             9
        3   2     2 3                                2 3       3   2   3   2 3
      5 6 4 5 6 4 5
      8 9   8       9             1 7                5 6
                                                       9
                                                           4 5
                                                             8
                                                                 4 5
                                                                   8
                                                                       6 4 5 6
                                                                       9   8 9
  1       1     1                                  1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7             8  9           7
                                                     5 6
                                                       93 24 5
                                                           7
  1     3 1                            3         3                         1       3

  7     9
          4
                      6
                      4
                      7                9
                                           4
                                               9    8 2 5                  4
                                                                           7     9
  1     3       1 2 3   2              3     2 3 1 2 3 1   3               1   2 3

  7     9
      5 6       4 5   4 5
                      7
                                           4   6
                                                 7      8
                                                   5 6 4 5
                                                       7
                                                                           4
                                                                           7
                                                                               5 6

  1                                          2   1 2         1 2           1   2
      5
      8 3 7 6                              4       5
                                                      9      4 5
                                                               8
                                                                           4   5
                                                                               8
                  1       3            3         1   3 1   3 1         3   1       3

      2 7     5   4
                        9
                              4
                                   8   9
                                                     6 4
                                                     9   8
                                                             4
                                                               8
                                                                       6
                                                                       9
                                                                           4
                                                                             8
                                                                                   6
                                                                                   9
  1   3   1 2     1   2 3          2   3               1   3 1 2       3   1 2     3
    5 6
  7 8 9       1 4
          4 5 6
            8
                  4   5
                        9
                              4
                              7
                                   5
                                   8   9
                                                       4 5
                                                       7 8
                                                             4 5
                                                             7 8
                                                                       6
                                                                       9
                                                                           4 5
                                                                           7 8
                                                                                   6
                                                                                   9
  1   3   1 2     1   2 3          2   3     2 3 1 2 3       1 2       3
    5 6
  7 8 9
          4 5 6
            8
                  4   5
                        9
                              4
                              7
                                   5
                                   8   9
                                           4   6
                                               9 7
                                                   5 6
                                                     9         6
                                                             4 5
                                                             7 8
                                                                       6
                                                                       9       4
      Back to Start               Skip Animation


                                                     Helmut Simonis            Visualization Techniques   93
                                                      Introduction
                                      Visualization by Annotation
                                           Visualization Interface
                                                     Conclusions


Propagation Steps (Bounds Consistency)
          1 2                      2 3       2 3 1 2 3   1   3 1 2   3 1 2 3

      4     5 6
                      8       7
                                   5
                                     9
                                               6
                                               9 7
                                                   5 6
                                                     9   7
                                                             5
                                                               7
                                                                 5   6
                                                                     9 7
                                                                         5 6
                                                                           9
        3   2     2 3                              2 3       3   2   3   2 3
      5 6 4 5 6 4 5
      8 9   8       9             1 7              5 6
                                                     9
                                                         4 5
                                                           8
                                                               4 5
                                                                 8
                                                                     6 4 5 6
                                                                     9   8 9
  1       1     1                                1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7             89           7
                                                   5 6
                                                     93 24 5
                                                         7
  1     3 1                          3         3                       1       3

  7     9
          4
                      6
                      4
                      7              9
                                         4
                                             9    8 2 5                4
                                                                       7     9
  1     3       1 2 3   2            3     2 3 1 2 3 1   3             1   2 3

  7     9
      5 6       4 5   4 5
                      7
                                         4   6
                                               7      8
                                                 5 6 4 5
                                                     7
                                                                       4
                                                                       7
                                                                           5 6

  1                                        2   1 2         1 2         1   2
      5
      8 3 7 6                            4       5
                                                    9      4 5
                                                             8
                                                                       4   5
                                                                           8
                  1     3 3                    1   3 1   3 1         3 1   3

      2 7     5   4
                  9
                    4
                      8 9
                                                   6 4
                                                   9   8
                                                           4
                                                             8
                                                                     6 4
                                                                     9
                                                                           6
                                                                         8 9
      3   2     2 3   2 3                                3   2       3   2 3
    5 6
  7 8 9
          5 6
          8   1 4
                5     5
                  9 7 8 9
                                                       5
                                                     7 8
                                                             5
                                                           7 8
                                                                     6   5 6
                                                                     9 7 8 9
  1   3 1 2   1 2 3   2 3                  2 3 1 2 3       1 2       3
    5 6 4 5 6 4 5
  7 8 9   8
                    4 5
                  9 7 8 9
                                         4   6
                                             9 7
                                                 5 6
                                                   9         6
                                                           4 5
                                                           7 8
                                                                     6
                                                                     9     4
      Back to Start               Skip Animation


                                                   Helmut Simonis          Visualization Techniques   94
                                                      Introduction
                                      Visualization by Annotation
                                           Visualization Interface
                                                     Conclusions


Propagation Steps (Bounds Consistency)
          1 2                      2 3       2 3 1 2 3   1           1 2 3
                                                                 3 1 2

      4     5 6
                      8       7
                                   5
                                     9
                                               6
                                               9 7
                                                   5 6
                                                     9   7
                                                             5     6
                                                                   9 7
                                                                   7
                                                                       5 6
                                                                         9
        3   2     2 3                              2 3       3   2     2 3
      5 6 4 5 6 4 5
      8 9   8       9             1 7              5 6
                                                     9
                                                         4 5
                                                           8
                                                               4   6 4 5 6
                                                                   9   8 9
  1       1     1                                1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7             89           7
                                                   5 6
                                                     93 24 5
                                                         7
  1     3 1                          3         3                     1   3

  7     9
          4
                      6
                      4
                      7              9
                                         4
                                             9    8 2 5              4
                                                                     7   9
  1     3       1 2 3   2            3     2 3 1 2 3     1   3       1 2 3

  7     9
      5 6       4 5   4 5
                      7
                                         4   6
                                               7
                                                 5 6
                                                      8  4 5
                                                         7
                                                                     4 5 6
                                                                     7
  1                                        2   1 2             1 2   1 2
      5
      8 3 7 6                            4       5
                                                    9          4     4 5
                                                                       8
                  1     3 3     1   3                    1   3 1     1   3

      2 7     5   4
                  9
                    4
                      8 9
                                    6
                                    9
                                                         4
                                                           8
                                                               4   6 4
                                                                   9
                                                                         6
                                                                       8 9
      3   2     2 3   2 3                                    3   2     2 3
    5 6
  7 8 9
          5 6
          8   1 4
                5     5
                  9 7 8 9
                                                           5
                                                         7 8   7
                                                                   6   5 6
                                                                   9 7 8 9
  1   3 1 2   1 2 3   2 3   2 3 1 2 3                          1 2
    5 6 4 5 6 4 5
  7 8 9   8
                    4 5
                  9 7 8 9
                          4   6
                              9 7
                                  5 6
                                    9                        6 4
                                                               7
                                                                   6
                                                                   9     4
      Back to Start               Skip Animation


                                                   Helmut Simonis        Visualization Techniques   95
                                                        Introduction
                                        Visualization by Annotation
                                             Visualization Interface
                                                       Conclusions


Propagation Steps (Bounds Consistency)
            1 2                      2 3       2 3 1 2 3     1           1 2 3
                                                                     3 1 2

      4       5 6
                        8       7
                                     5
                                       9
                                                 6
                                                 9 7
                                                     5 6
                                                       9     7
                                                                 5     6
                                                                       9 7
                                                                       7
                                                                           5 6
                                                                             9
        3   2     2 3                                2 3         3   2     2 3
      5 6 4 5 6 4 5
      8 9   8       9               1 7              5 6
                                                       9
                                                             4 5
                                                               8
                                                                   4   6 4 5 6
                                                                       9   8 9
  1       1     1                                  1         1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7               89           7
                                                     5 6
                                                       9   3 2
                                                             4 5
                                                             7
  1     3 1                            3         3                       1   3

  7     9
          4           4
                      7 6              9
                                           4
                                               9       8 2 5             4
                                                                         7   9
  1     3       1 2 3   2              3     2 3 1 2 3       1   3       1 2 3

  7     9
      5 6       4 5   4 5
                      7
                                           4   6
                                                 7
                                                   5 6
                                                           8 4 5
                                                             7
                                                                         4 5 6
                                                                         7
  1                                          2   1 2               1 2   1 2
      5
      8 3 7 6                              4       5
                                                         9         4     4 5
                                                                           8
                    1       3
                            3                      1     3   1   3 1     1   3

      2 7     5     4
                      9
                        4
                          8 9
                                                         6
                                                         9
                                                             4
                                                               8
                                                                   4   6 4
                                                                       9
                                                                             6
                                                                           8 9
          3   2     2 3   2 3                                    3   2     2 3
    5
  7 8
          6
          9   1 4
              5 6
              8
                    5     5
                      9 7 8 9
                                                               5
                                                             7 8   7
                                                                       6   5 6
                                                                       9 7 8 9
  1       3 1 2   1 2 3   2 3                  2 3 1 2 3           1 2
    5
  7 8     9
              5
              8
                    5     5
                      9 7 8 9                    9 7
                                                     5
                                                       9         6     7     9   4
      Back to Start                 Skip Animation


                                                       Helmut Simonis            Visualization Techniques   96
                                              Introduction
                              Visualization by Annotation
                                   Visualization Interface
                                             Conclusions


Propagation Steps (Bounds Consistency)
          1 2              2 3    2 3 1 2 3    1           1
                                                       3 1 2   3

      4     5 6
                  8   7
                           5
                             9
                                    6
                                    9 7
                                        5 6
                                          9    7
                                                   5     6
                                                         9 7
                                                         7
                                                             5 6
                                                               9
        3   2     2 3                   2 3        3   2       3
      5 6 4 5 6 4 5
      8 9   8       9     1 7           5 6
                                          9
                                               4 5
                                                 8
                                                     4   6
                                                         9
                                                             5 6
                                                             8 9
          1     1                     1        1

      7   4 5 6 4 5   4 5
                    9 7   9 8         7
                                        5 6
                                          9 3 24 5
                                               7
  1     3 1               3         3                      1   3

  7     9
          4
                  6   4
                      7   9
                            4
                                9       8 2 5                  7     9
  1     3       1 2 3   2 3   2 3 1        2 3 1   3           1     3

  7     9
      5 6       4 5   4 5
                      7
                            4   6
                                  7         8
                                           5 6 4 5
                                               7               7
                                                                   5 6

  1                           2   1        2         1 2       1
      5
      8 3 7 6               4
                                          95         4       5
                                                             8
                1   3     3       1          3 1   3 1     1   3

      2 7     5 4
                    9
                      4
                        8 9
                                             6 4
                                             9   8
                                                     4   6
                                                         9
                                                               6
                                                             8 9
        3   2     2 3   2 3                        3   2       3

  7
      5 6
      8 9   8 1 4
            5 6   5     5
                    9 7 8 9
                                                 5
                                               7 8   7
                                                         6   5 6
                                                         9 7 8 9
  1     3 1 2   1 2 3   2 3   2 3 1        2 3       1 2

  7
      5
      8 9
            5
            8
                  5     5
                    9 7 8 9     9 7
                                           5
                                             9     6 7   9         4
      Back to Start       Skip Animation


                                           Helmut Simonis          Visualization Techniques   97
                                                          Introduction
                                          Visualization by Annotation
                                               Visualization Interface
                                                         Conclusions


Propagation Steps (Bounds Consistency)
            1 2                        2 3       2 3 1 2 3   1           1
                                                                     3 1 2   3

      4       5 6
                          8       7
                                       5
                                         9
                                                   6
                                                   9 7
                                                       5 6
                                                         9   7
                                                                 5     6
                                                                       9 7
                                                                       7
                                                                           5 6
                                                                             9
        3       2         2 3                          2 3       3   2       3
      5 6
        9
                5 6       5
                            9         1 7              5 6
                                                         9
                                                             4 5
                                                               8
                                                                   4   6
                                                                       9
                                                                           5 6
                                                                           8 9
            1         1                              1       1

      7         5 6       5
                              9
                                  4 5
                                        89
                                                       5 6
                                                         9   3 2
                                                             4 5

  1   3 1                                3         3                         1       3

      9
        4
                          6     9
                                  4
                                  7   9
                                             4
                                                         8 2 5               7     9
  1   3               1 2 3   2 3   2 3 1                2 3 1   3           1     3
    5 6
        9             4 5   4 5
                            7
                                  4   6
                                        7                    8
                                                         5 6 4 5
                                                             7               7
                                                                                 5 6

  1                                 2   1                2         1 2       1
      5
      8 3 7 6                     4                      5
                                                           9       4     5
                                                                         8
                      1       3          3           1   3 1   3 1     1   3

      2 7     5       4
                      9
                        4
                          8 9
                                                         6 4
                                                         9   8
                                                                 4   6
                                                                     9
                                                                           6
                                                                         8 9
          3   2     2 3   2 3                                  3   2       3
      5
      8
          6
          9   1 4
              5 6
              8
                    5     5
                      9 7 8 9
                                                             5
                                                           7 8   7
                                                                     6   5 6
                                                                     9 7 8 9
  1       3 1 2   1 2 3   2 3                    2 3 1 2 3       1 2
      5
      8   9
              5
              8
                    5     5
                      9 7 8 9                      9 7
                                                       5
                                                         9       6
                                                                 7   9           4
      Back to Start                   Skip Animation


                                                         Helmut Simonis          Visualization Techniques   98
                                                          Introduction
                                          Visualization by Annotation
                                               Visualization Interface
                                                         Conclusions


Propagation Steps (Bounds Consistency)
            1 2                        2 3       2 3       2 3 1   3 1 2   1   3

      4       5 6
                          8            5
                                         9
                                                   6
                                                   9
                                                           5 6
                                                             9 7
                                                                 5
                                                                     7
                                                                         6
                                                                         9 7
                                                                             5 6
                                                                               9
        3       2         2 3                              2 3     3   2       3
      5 6
        9
                5 6       5
                            9         1 7                  5 6 4 5
                                                             9   8
                                                                     4   6
                                                                         9
                                                                             5 6
                                                                             8 9
            1         1                                        1

      7         5 6       5
                              9
                                  4 5
                                        89                     3 2
                                                           5 6 4 5
                                                             9
  1   3 1                                3         3                       1   3

      9
        4
                          6     9
                                  4
                                  7   9
                                             4
                                                           8 2 5            7     9
  1   3               1 2 3   2 3   2 3 1                  2 3 1   3        1     3
    5 6
        9             4 5   4 5
                            7
                                  4   6
                                        7                      8
                                                           5 6 4 5
                                                               7            7
                                                                                5 6

  1                                 2   1                  2         1 2    1
      5
      8 3 7 6                     4                        5
                                                             9       4   5
                                                                         8
                      1       3          3             1 3 1   3 1     1   3

      2 7     5       4
                      9
                        4
                          8 9
                                                         6 4
                                                         9   8
                                                                 4   6
                                                                     9
                                                                           6
                                                                         8 9
          3   2     2 3   2 3                                  3   2       3
      5
      8
          6
          9   1 4
              5 6
              8
                    5     5
                      9 7 8 9
                                                             5
                                                           7 8   7
                                                                     6   5 6
                                                                     9 7 8 9
  1       3 1 2   1 2 3   2 3                    2 3 1 2 3       1 2
      5
      8   9
              5
              8
                    5     5
                      9 7 8 9                      9 7
                                                       5
                                                         9      67   9          4
      Back to Start                   Skip Animation


                                                           Helmut Simonis       Visualization Techniques   99
                                                          Introduction
                                          Visualization by Annotation
                                               Visualization Interface
                                                         Conclusions


Propagation Steps (Bounds Consistency)
            1 2                        2 3       2 3       2 3 1     1        1

      4       5 6
                          8            5
                                         9
                                                   6
                                                   9
                                                           5 6
                                                             9 7
                                                                 5
                                                                     7
                                                                            6
                                                                            9 7
                                                                                5 6
                                                                                  9
        3       2         2 3                              2 3
      5 6
        9
                5 6       5
                            9         1 7                  5 6 4 5
                                                             9   8
                                                                     4      6
                                                                            9
                                                                                    5 6
                                                                                    8 9
            1         1                                        1

      7         5 6       5
                              9
                                  4 5
                                        89                     3 2
                                                           5 6 4 5
                                                             9
                                         3         3                            1       3

      1         4 6               4
                                  7   9     9
                                             4
                                                           8 2 5                7     9
                                    2 3   2 3 1            2 3 1   3            1     3

      5         9 2               4 5
                                  7
                                        4   6
                                              7                8
                                                           5 6 4 5
                                                               7                7
                                                                                    5 6

                                          2   1            2         1 2        1

      8         3 7 6                   4                  5
                                                             9       4   5
                                                                         8
                      1       3          3             1 3 1   3 1     1   3

      2         7     5
                      4
                      9
                        4
                          8 9
                                                         6 4
                                                         9   8
                                                                 4   6
                                                                     9
                                                                           6
                                                                         8 9
          3   2     2 3   2 3                                  3   2       3
      5
      8
          6
          9
              5 6
              8
                    5
                      1 4 5
                      9 7 8 9
                                                             5
                                                           7 8   7
                                                                     6   5 6
                                                                     9 7 8 9
  1       3 1 2   1 2 3   2 3                    2 3 1 2 3       1 2
      5
      8   9
              5
              8
                    5     5
                      9 7 8 9                      9 7
                                                       5
                                                         9      67   9              4
      Back to Start                   Skip Animation


                                                           Helmut Simonis           Visualization Techniques   100
                                                       Introduction
                                       Visualization by Annotation
                                            Visualization Interface
                                                      Conclusions


Propagation Steps (Bounds Consistency)
           1 2                                      2 3 1           1     1

   4         5 6
                       8 5                    6     5 6
                                                      9 7
                                                          5
                                                                    7
                                                                        6
                                                                        9 7
                                                                            5 6
                                                                              9
       3     2             3                        2 3
       6
       9
             5 6       5
                         1 9                  7     5 6 4 5
                                                      9   8
                                                                    4   6
                                                                        9
                                                                                5 6
                                                                                8 9
                   1                                    1

   7        6          5
                         4 9                  8 9   3 2 4 5

                                      3         3                                 3

   1        4          6       7      9         8 2 5
                                                9                           7     9
                                      3         3       1       3

   5        9          2       4
                               7
                                          4
                                                1
                                                6
                                                    8 6 4
                                                        7


   8        3          7 6                    2 5 9 4 1
                                      3                 1       3 1     3   1

   2        7          4
                       8
                               4
                                      9       5 6       4
                                                            8
                                                                  4     6
                                                                        6
                                                                      8 9
                                                                        9
           2       3   2              3                     3   2       3

   6       5 6
           8
                 5     5
                   9 7 8              9       1 4         5
                                                        7 8   7
                                                                  6   5 6
                                                                  9 7 8 9
       3 1 2   1   3   2              3       2 3             1 2

       9
           5
           8
                 5     5
                   9 7 8              9         7 6
                                                9     4             7   9


   Back to Start                   Skip Animation


                                                    Helmut Simonis              Visualization Techniques   101
                                                      Introduction
                                      Visualization by Annotation
                                           Visualization Interface
                                                     Conclusions


Propagation Steps (Bounds Consistency)
           1 2                                    2 3 1             1

   4                 8 5                      6         7           7   9 7       9
       3     2           3                        2 3

       9
             5
                       1 9                    7         4 5
                                                          8
                                                                        6
                                                                        9
                                                                                5
                                                                                8 9
                 1                                      1

   7        6        5
                       4                      8 9   3 2   5

                                      3       3                                   3

   1        4        6       7        9       9 8 2 5                       7     9
                                      3       3                 3

   5        9        2       7
                                          4
                                                1   8 6 4
                                                        7


   8        3        7 6                      2 5 9 4 1
                                      3                 1       3 1               3

   2        7        4            8 9         5 6           8         8 9
                                                                        9
           2             3        2 3                       3   2       3

   6       5
           8             9 7 8 9              1 4         5
                                                        7 8   7
                                                                      5
                                                                  9 7 8 9
       3 1 2     1           2                3               1 2

       9
           5
           8
                     5
                                  8           9 7 6   4
   Back to Start                 Skip Animation


                                                  Helmut Simonis                Visualization Techniques   102
                                                      Introduction
                                      Visualization by Annotation
                                           Visualization Interface
                                                     Conclusions


Propagation Steps (Bounds Consistency)
           1 2                                    2 3 1             1

   4                 8 5                      6         7           7   9 7       9
       3     2           3                        2 3

       9
             5
                       1 9                    7         4 5
                                                          8
                                                                        6
                                                                        9
                                                                                5
                                                                                8 9
                 1                                      1

   7        6        5
                       4                      8 9   3 2   5

                                      3       3                                   3

   1        4        6       7        9       9 8 2 5                       7
                                      3       3                 3

   5        9        2       7
                                          4
                                                1   8 6 7


   8        3        7 6                      2 5 9 4 1
                                      3                 1       3 1               3

   2        7        4            8 9         5 6           8         8 9
                                                                        9
           2             3        2 3                       3   2       3

   6       5
           8             9 7 8 9              1 4         5
                                                        7 8   7
                                                                      5
                                                                  9 7 8 9
       3 1 2     1           2                3               1 2

       9
           5
           8
                     5
                                  8           9 7 6   4
   Back to Start                 Skip Animation


                                                  Helmut Simonis                Visualization Techniques   103
                                                      Introduction
                                      Visualization by Annotation
                                           Visualization Interface
                                                     Conclusions


Propagation Steps (Bounds Consistency)
           1 2                                    2 3 1             1

   4                 8 5                      6         7           7   9 7       9
       3     2           3                        2 3

       9
             5
                       1 9                    7         4 5
                                                          8
                                                                        6
                                                                        9
                                                                                5
                                                                                8 9
                 1                                      1

   7         6       5
                       4                      8 9   3 2   5

                                      3       3                                   3

   1         4       6       7        9       9 8 2 5                       7
                                      3       3                 3

   5         9       2       7
                                          4
                                                1   8 6 7


   8         3       7 6                      2 5 9 4 1
                                      3                 1       3 1               3

   2         7       4            8 9         5 6           8         8 9
                                                                        9
                         3        2 3                       3   2       3

   6         5
             8           9 7 8 9              1 4         5
                                                        7 8   7
                                                                      5
                                                                  9 7 8 9
       3 1       1           2                3               1 2

       9
             5
             8
                     5
                                  8           9 7 6   4
   Back to Start                 Skip Animation


                                                  Helmut Simonis                Visualization Techniques   104
                                                      Introduction
                                      Visualization by Annotation
                                           Visualization Interface
                                                     Conclusions


Propagation Steps (Bounds Consistency)
           1 2                                    2 3 1             1

   4                 8 5                      6         7           7   9 7       9
       3     2           3                        2 3

       9
             5
                       1 9                    7         4 5
                                                          8
                                                                        6
                                                                        9
                                                                                5
                                                                                8 9
                 1                                      1

   7         6       5
                       4                      8 9   3 2   5

                                      3       3                                   3

   1         4       6       7        9       9 8 2 5                       7
                                      3       3                 3

   5         9       2       7
                                          4
                                                1   8 6 7


   8         3       7 6                      2 5 9 4 1
                                      3                 1       3 1               3

   2         7       4            8 9         5 6           8         8 9
                                                                        9
                         3        2 3                       3   2       3

   6         5
             8           9        8 9         1 4         5
                                                        7 8   7
                                                                      5
                                                                  9 7 8 9
       3 1       1                2           3               1 2

       9
             5
             8
                     5
                                  8           9 7 6   4
   Back to Start                 Skip Animation


                                                  Helmut Simonis                Visualization Techniques   105
                                                     Introduction
                                     Visualization by Annotation
                                          Visualization Interface
                                                    Conclusions


Propagation Steps (Bounds Consistency)
           1 2                                   2 3 1             1

   4                 8 5                     6         7           7   9 7       9
       3     2           3                       2 3

       9
             5
                       1 9                   7         4 5
                                                         8
                                                                       6
                                                                       9
                                                                               5
                                                                               8 9
                 1                                     1

   7         6       5
                       4                     8 9   3 2   5

                                     3       3                                   3

   1         4       6       7       9       9 8 2 5                       7
                                     3       3                 3

   5         9       2       7
                                         4
                                               1   8 6 7


   8         3       7 6                     2 5 9 4 1
                                     3                 1       3 1               3

   2         7       4           8 9         5 6           8         8 9
                                                                       9
                         3       2 3                       3   2       3

   6         5
             8           9       8 9         1 4         5
                                                       7 8   7
                                                                     5
                                                                 9 7 8 9
       3 1       1               2           3               1 2

       9
             5
             8
                     5
                                 8           9 7 6   4
   Back to Start


                                                 Helmut Simonis                Visualization Techniques   106
                                                     Introduction
                                     Visualization by Annotation
                                          Visualization Interface
                                                    Conclusions


After Setup (Bounds Consistency)
           1 2                                   2 3 1             1

   4                 8 5                     6         7           7   9 7       9
       3     2           3                       2 3

       9
             5
                       1 9                   7         4 5
                                                         8
                                                                       6
                                                                       9
                                                                               5
                                                                               8 9
                 1                                     1

   7         6       5
                       4                     8 9   3 2   5

                                     3       3                                   3

   1         4       6       7       9       9 8 2 5                       7
                                     3       3                 3

   5         9       2       7
                                         4
                                               1   8 6 7


   8         3       7 6                     2 5 9 4 1
                                     3                 1       3 1               3

   2         7       4           8 9         5 6           8         8 9
                                                                       9
                         3       2 3                       3   2       3

   6         5
             8           9       8 9         1 4         5
                                                       7 8   7
                                                                     5
                                                                 9 7 8 9
       3 1       1               2           3               1 2

       9
             5
             8
                     5
                                 8           9 7 6   4

                                                 Helmut Simonis                Visualization Techniques   107
                                                           Introduction
                                           Visualization by Annotation
                                                Visualization Interface
                                                          Conclusions


Propagation Steps (Domain Consistency)
               1   2   3               1 2 3 1 2 3 1   2   3   1   2   3   1   2   3   1   2   3

      4        4
               7
                   5
                   8
                       6
                       9       8       4 5 6 4 5 6 4
                                       7 8 9 7 8 9 7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2    3   1   2   3   1   2   3               1   2   3   1   2   3   1   2   3   1   2   3
  4
  7
      5
      8
           6
           9
               4
               7
                   5
                   8
                       6
                       9
                           4
                           7
                               5
                               8
                                   6
                                   9    1 7        4
                                                   7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2    3   1   2   3   1   2   3   1 2 3       1   2   3   1   2   3
  4
  7
      5
      8
           6
           9
               4
               7
                   5
                   8
                       6
                       9
                           4
                           7
                               5
                               8
                                   6
                                   9      8
                                       4 5 6
                                       7 8 9
                                                   4
                                                   7
                                                       5
                                                       8   3 2
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
  1   2    3   1   2   3               1 2 3 1 2 3                                     1   2   3
  4
  7
      5
      8
           6
           9
               4
               7
                   5
                   8
                       6
                       9       6       4 5 6 4 5 6
                                       7 8 9 7 8 9     8 2 5                           4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2    3               1 2 3       1 2 3 1 2 3 1   2   3   1 2 3                   1   2   3
  4
  7
      5
      8 9  6
           9
                           4 5 6
                           7 8 9
                                       4 5 6 4 5 6 4
                                       7 8 9 7 8 9 7
                                                       5
                                                       8   8
                                                           6
                                                           9
                                                               4 5 6
                                                               7 8 9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2    3                                 1 2 3 1   2   3               1   2   3   1   2   3
  4
  7
      5
      8 3 7 6
           6
           9
                                             4 5 6 4
                                             7 8 9 7
                                                       5
                                                       8 9 6
                                                           9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
                           1   2   3   1 2 3       1   2   3   1   2   3   1   2   3   1   2   3

      2 7     5            4
                           7
                               5
                               8
                                   6
                                   9
                                       4 5 6
                                       7 8 9
                                                   4
                                                   7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2    3   1   2   3   1   2   3   1 2 3                   1   2   3   1   2   3   1   2   3
  4
  7
      5
      8
           6
           9  1 4
               4
               7
                   5
                   8
                       6
                       9
                           4
                           7
                               5
                               8
                                   6
                                   9
                                       4 5 6
                                       7 8 9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2    3   1   2   3   1   2   3   1 2 3 1 2 3 1   2 3                 1   2   3
  4
  7
      5
      8
           6
           9
               4
               7
                   5
                   8
                       6
                       9
                           4
                           7
                               5
                               8
                                   6
                                   9
                                       4 5 6 4 5 6 4
                                       7 8 9 7 8 9 7
                                                       5 6
                                                       8 9         6       4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9       4
          Skip Animation


                                                       Helmut Simonis                      Visualization Techniques   108
                                                          Introduction
                                          Visualization by Annotation
                                               Visualization Interface
                                                         Conclusions


Propagation Steps (Domain Consistency)
              1   2   3               1 2 3 1 2 3 1    2   3   1   2   3   1   2   3   1   2   3

      4       4
              7
                  5
                  8
                      6
                      9       8       4 5 6 4 5 6 4
                                      7 8 9 7 8 9 7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3   1   2   3   1   2   3               1    2   3   1   2   3   1   2   3   1   2   3
  4
  7
      5
      8
          6
          9
              4
              7
                  5
                  8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9    1 7        4
                                                  7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3   1   2   3   1   2   3   1 2 3       1    2   3   1   2   3
  4
  7
      5
      8
          6
          9
              4
              7
                  5
                  8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9      8
                                      4 5 6
                                      7 8 9
                                                  4
                                                  7
                                                       5
                                                       8  3 2
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
  1   2   3   1   2   3               1 2 3 1 2 3                                      1   2   3
  4
  7
      5
      8
          6
          9
              4
              7
                  5
                  8
                      6
                      9       6       4 5 6 4 5 6
                                      7 8 9 7 8 9     8 2 5                            4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3               1 2 3       1 2 3 1 2 3 1    2   3   1 2 3                   1   2   3
  4
  7
      5
      8 9 6
          9
                          4 5 6
                          7 8 9
                                      4 5 6 4 5 6 4
                                      7 8 9 7 8 9 7
                                                       5
                                                       8  86
                                                           9
                                                               4 5 6
                                                               7 8 9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3                                 1 2 3 1    2   3               1   2   3   1   2   3
  4
  7
      5
      8 3 7 6
          6
          9
                                            4 5 6 4
                                            7 8 9 7
                                                       5
                                                       89  6
                                                           9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
                          1   2   3   1 2 3       1    2   3   1   2   3   1   2   3   1   2   3

      2 7     5           4
                          7
                              5
                              8
                                  6
                                  9
                                      4 5 6
                                      7 8 9
                                                  4
                                                  7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3   1   2   3   1   2   3   1 2 3                    1   2   3   1   2   3   1   2   3
  4
  7
      5
      8
          6
          9   1 4
              4
              7
                  5
                  8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9
                                      4 5 6
                                      7 8 9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3   1   2   3   1   2   3   1 2 3 1 2 3 1    2 3                 1   2   3
  4
  7
      5
      8
          6
          9
              4
              7
                  5
                  8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9
                                      4 5 6 4 5 6 4
                                      7 8 9 7 8 9 7
                                                       5 6
                                                       8 9         6       4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9       4
      Back to Start                   Skip Animation


                                                       Helmut Simonis                      Visualization Techniques   109
                                                          Introduction
                                          Visualization by Annotation
                                               Visualization Interface
                                                         Conclusions


Propagation Steps (Domain Consistency)
              1 2     3               1 2 3 1 2 3 1    2 3     1 2     3   1 2     3   1 2     3

      4       7
                5     6
                      9       8       7
                                        5 6
                                          9 7
                                              5 6
                                                9 7
                                                       5 6
                                                         9     7
                                                                 5     6
                                                                       9   7
                                                                             5     6
                                                                                   9   7
                                                                                         5     6
                                                                                               9
  1   2   3   1 2     3   1   2   3               1    2 3     1 2     3   1 2     3   1 2     3
  4
  7
      5
      8
          6
          9
              4 5
              7 8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9    1 7        4
                                                  7
                                                       5 6
                                                       8 9
                                                               4 5
                                                               7 8
                                                                       6
                                                                       9
                                                                           4 5
                                                                           7 8
                                                                                   6
                                                                                   9
                                                                                       4 5
                                                                                       7 8
                                                                                               6
                                                                                               9
  1   2   3   1 2     3   1   2   3   1 2 3       1    2 3     1 2     3
  4
  7
      5
      8
          6
          9
              4 5
              7 8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9      8
                                      4 5 6
                                      7 8 9
                                                  4
                                                  7
                                                       5 6
                                                       8 93 2  4 5
                                                               7 8
                                                                       6
                                                                       9
  1   2   3   1 2     3               1 2 3 1 2 3                                      1   2   3
  4
  7
      5
      8
          6
          9
              4 5
              7 8
                      6
                      9       6       4 5 6 4 5 6
                                      7 8 9 7 8 9     8 2 5                            4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3               1 2 3       1 2 3 1 2 3 1    2   3   1 2 3                   1   2   3
  4
  7
      5
      8 9 6
          9
                          4 5 6
                          7 8 9
                                      4 5 6 4 5 6 4
                                      7 8 9 7 8 9 7
                                                       5
                                                       8  86
                                                           9
                                                               4 5 6
                                                               7 8 9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3                                 1 2 3 1    2   3               1   2   3   1   2   3
  4
  7
      5
      8 3 7 6
          6
          9
                                            4 5 6 4
                                            7 8 9 7
                                                       5
                                                       89  6
                                                           9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
                          1   2   3   1 2 3       1    2   3   1   2   3   1   2   3   1   2   3

      2 7     5           4
                          7
                              5
                              8
                                  6
                                  9
                                      4 5 6
                                      7 8 9
                                                  4
                                                  7
                                                       5
                                                       8
                                                           6
                                                           9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3   1   2   3   1   2   3   1 2 3                    1   2   3   1   2   3   1   2   3
  4
  7
      5
      8
          6
          9   1 4
              4
              7
                  5
                  8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9
                                      4 5 6
                                      7 8 9
                                                               4
                                                               7
                                                                   5
                                                                   8
                                                                       6
                                                                       9
                                                                           4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9
                                                                                       4
                                                                                       7
                                                                                           5
                                                                                           8
                                                                                               6
                                                                                               9
  1   2   3   1   2   3   1   2   3   1 2 3 1 2 3 1    2 3                 1   2   3
  4
  7
      5
      8
          6
          9
              4
              7
                  5
                  8
                      6
                      9
                          4
                          7
                              5
                              8
                                  6
                                  9
                                      4 5 6 4 5 6 4
                                      7 8 9 7 8 9 7
                                                       5 6
                                                       8 9         6       4
                                                                           7
                                                                               5
                                                                               8
                                                                                   6
                                                                                   9       4
      Back to Start                   Skip Animation


                                                       Helmut Simonis                      Visualization Techniques   110
                                                      Introduction
                                      Visualization by Annotation
                                           Visualization Interface
                                                     Conclusions


Propagation Steps (Domain Consistency)
          1 2     3               1 2 3 1 2 3 1    2 3     1 2     3   1 2     3   1 2     3

      4   7
            5     6
                  9       8       7
                                    5 6
                                      9 7
                                          5 6
                                            9 7
                                                   5 6
                                                     9     7
                                                             5     6
                                                                   9   7
                                                                         5     6
                                                                               9   7
                                                                                     5     6
                                                                                           9
  1   3   1 2     3   1   2   3               1    2 3     1 2     3   1 2     3   1 2     3
    5 6
  7 8 9
          4 5
          7 8
                  6
                  9
                      4
                      7
                          5
                          8
                              6
                              9    1 7        4
                                              7
                                                   5 6
                                                   8 9
                                                           4 5
                                                           7 8
                                                                   6
                                                                   9
                                                                       4 5
                                                                       7 8
                                                                               6
                                                                               9
                                                                                   4 5
                                                                                   7 8
                                                                                           6
                                                                                           9
  1   3   1 2     3   1   2   3   1 2 3       1    2 3     1 2     3
    5 6
  7 8 9
          4 5
          7 8
                  6
                  9
                      4
                      7
                          5
                          8
                              6
                              9      8
                                  4 5 6
                                  7 8 9
                                              4
                                              7
                                                   5 6
                                                   8 93 2  4 5
                                                           7 8
                                                                   6
                                                                   9
  1   3   1 2     3               1 2 3 1 2 3                                      1   2   3
    5 6
  7 8 9
          4 5
          7 8
                  6
                  9       6       4 5 6 4 5 6
                                  7 8 9 7 8 9     8 2 5                            4
                                                                                   7
                                                                                       5
                                                                                       8
                                                                                           6
                                                                                           9
  1   3               1 2 3       1 2 3 1 2 3 1    2   3   1 2 3                   1   2   3
    5 6
  7 8 9 9             4 5 6
                      7 8 9
                                  4 5 6 4 5 6 4
                                  7 8 9 7 8 9 7
                                                   5
                                                   8  86
                                                       9
                                                           4 5 6
                                                           7 8 9
                                                                                   4
                                                                                   7
                                                                                       5
                                                                                       8
                                                                                           6
                                                                                           9
  1   3                                 1 2 3 1    2   3               1   2   3   1   2   3
    5 6
  7 8 9 3 7 6                           4 5 6 4
                                        7 8 9 7
                                                   5
                                                   89  6
                                                       9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
                                                                                   4
                                                                                   7
                                                                                       5
                                                                                       8
                                                                                           6
                                                                                           9
                      1   2   3   1 2 3       1    2   3   1   2   3   1   2   3   1   2   3

      2 7     5       4
                      7
                          5
                          8
                              6
                              9
                                  4 5 6
                                  7 8 9
                                              4
                                              7
                                                   5
                                                   8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
                                                                                   4
                                                                                   7
                                                                                       5
                                                                                       8
                                                                                           6
                                                                                           9
  1   3   1   2   3   1   2   3   1 2 3                    1   2   3   1   2   3   1   2   3
    5 6
  7 8 9
          4
          7   1 4
              5
              8
                  6
                  9
                      4
                      7
                          5
                          8
                              6
                              9
                                  4 5 6
                                  7 8 9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
                                                                                   4
                                                                                   7
                                                                                       5
                                                                                       8
                                                                                           6
                                                                                           9
  1   3   1   2   3   1   2   3   1 2 3 1 2 3 1    2 3                 1   2   3
    5 6
  7 8 9
          4
          7
              5
              8
                  6
                  9
                      4
                      7
                          5
                          8
                              6
                              9
                                  4 5 6 4 5 6 4
                                  7 8 9 7 8 9 7
                                                   5 6
                                                   8 9         6       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9       4
      Back to Start               Skip Animation


                                                   Helmut Simonis                      Visualization Techniques   111
                                                        Introduction
                                        Visualization by Annotation
                                             Visualization Interface
                                                       Conclusions


Propagation Steps (Domain Consistency)
            1 2     3               1 2 3 1 2 3 1 2 3 1    2 3 1 2 3 1 2   3

      4     7
              5     6
                    9       8       7
                                      5 6
                                        9 7
                                            5 6
                                              9 7
                                                  5 6
                                                    9 7
                                                           5 6
                                                             9 7
                                                                 5 6
                                                                   9 7
                                                                       5   6
                                                                           9
        3     2     3     2     3                 2 3      2 3   2 3   2   3
      5 6
      8 9
            4 5
              8
                    6
                    9
                        4 5
                          8
                                6
                                9    1 7        4 5 6 4
                                                  8 9
                                                           5 6 4 5 6 4 5
                                                           8 9   8 9   8
                                                                           6
                                                                           9
  1     3   1 2     3   1 2     3   1 2 3       1 2 3 1    2 3

  7
      5 6
      8 9
            4 5
            7 8
                    6
                    9
                        4 5
                        7 8
                                6
                                9      8
                                    4 5 6
                                    7 8 9             3 2
                                                4 5 6 4
                                                7 8 9 7
                                                           5 6
                                                           8 9
  1     3   1 2     3               1 2 3 1 2 3                      1 2   3

  7
      5 6
      8 9
            4 5
            7 8
                    6
                    9       6       4 5 6 4 5 6
                                    7 8 9 7 8 9   8 2 5              4 5
                                                                     7 8
                                                                           6
                                                                           9
  1     3               1 2 3       1 2 3 1 2 3 1 2 3 1    2 3       1 2   3

  7     9
      5 6
      8 9
                        4 5 6
                        7 8 9                         8
                                    4 5 6 4 5 6 4 5 6 4
                                    7 8 9 7 8 9 7 8 9 7
                                                           5 6
                                                           8 9
                                                                     4 5
                                                                     7 8
                                                                           6
                                                                           9
  1     3                                 1 2 3 1 2 3          1 2 3 1 2   3

  7     3 7 6
      5 6
      8 9                                           9
                                          4 5 6 4 5 6
                                          7 8 9 7 8 9
                                                               4 5 6 4 5
                                                               7 8 9 7 8
                                                                           6
                                                                           9
                        1   2   3   1 2 3       1 2 3 1    2 3 1 2 3 1 2   3

      2 7     5         4
                        7
                            5
                            8
                                6
                                9
                                    4 5 6
                                    7 8 9
                                                4 5 6 4
                                                7 8 9 7
                                                           5 6 4 5 6 4 5
                                                           8 9 7 8 9 7 8
                                                                           6
                                                                           9
  1   3     1   2   3   1   2   3   1 2 3             1    2 3 1 2 3 1 2   3
    5 6
  7 8 9
            4
            7 1 4
                5
                8
                    6
                    9
                        4
                        7
                            5
                            8
                                6
                                9
                                    4 5 6
                                    7 8 9
                                                      4
                                                      7
                                                           5 6 4 5 6 4 5
                                                           8 9 7 8 9 7 8
                                                                           6
                                                                           9
  1   3     1   2   3   1   2   3   1 2 3 1 2 3 1 2 3          1 2 3
    5 6
  7 8 9
            4
            7
                5
                8
                    6
                    9
                        4
                        7
                            5
                            8
                                6
                                9
                                    4 5 6 4 5 6 4 5 6
                                    7 8 9 7 8 9 7 8 9     6    4 5 6
                                                               7 8 9   4
      Back to Start                 Skip Animation


                                                     Helmut Simonis    Visualization Techniques   112
                                                  Introduction
                                  Visualization by Annotation
                                       Visualization Interface
                                                 Conclusions


Propagation Steps (Domain Consistency)
            1 2               1 2 3 1 2 3 1 2 3 1    2 3 1 2 3 1 2   3

      4       5 6
                    8         7
                                5 6
                                  9 7
                                      5 6
                                        9 7
                                            5 6
                                              9 7
                                                     5 6
                                                       9 7
                                                           5 6
                                                             9 7
                                                                 5   6
                                                                     9
        3     2     2 3                     2 3      2 3   2 3   2   3
      5 6
      8 9
            4 5 6 4 5 6
              8     8 9        1 7        4 5 6 4
                                            8 9
                                                     5 6 4 5 6 4 5
                                                     8 9   8 9   8
                                                                     6
                                                                     9
  1     3   1 2   1 2 3       1 2 3       1 2 3 1    2 3

  7
      5 6
      8 9
            4 5 6 4 5 6
              8   7 8 9          8
                              4 5 6
                              7 8 9             3 2
                                          4 5 6 4
                                          7 8 9 7
                                                     5 6
                                                     8 9
  1     3   1 2               1 2 3 1 2 3                      1 2   3

  7
      5 6
      8 9
            4 5 6
              8     6         4 5 6 4 5 6
                              7 8 9 7 8 9   8 2 5              4 5
                                                               7 8
                                                                     6
                                                                     9
  1     3         1 2 3       1 2 3 1 2 3 1 2 3 1    2 3       1 2   3

  7     9
      5 6
      8 9
                  4 5 6
                  7 8 9                         8
                              4 5 6 4 5 6 4 5 6 4
                              7 8 9 7 8 9 7 8 9 7
                                                     5 6
                                                     8 9
                                                               4 5
                                                               7 8
                                                                     6
                                                                     9
  1     3                           1 2 3 1 2 3          1 2 3 1 2   3

  7     3 7 6
      5 6
      8 9                                     9
                                    4 5 6 4 5 6
                                    7 8 9 7 8 9
                                                         4 5 6 4 5
                                                         7 8 9 7 8
                                                                     6
                                                                     9
                1     2   3   1 2 3       1 2 3 1    2 3 1 2 3 1 2   3

      2 7     5 4
                7
                      5
                      8
                          6
                          9
                              4 5 6
                              7 8 9
                                          4 5 6 4
                                          7 8 9 7
                                                     5 6 4 5 6 4 5
                                                     8 9 7 8 9 7 8
                                                                     6
                                                                     9
  1     3 1 2   1     2   3   1 2 3             1    2 3 1 2 3 1 2   3

  7   8 9   8 1 4
      5 6 4 5 6 4
                7
                      5
                      8
                          6
                          9
                              4 5 6
                              7 8 9
                                                4
                                                7
                                                     5 6 4 5 6 4 5
                                                     8 9 7 8 9 7 8
                                                                     6
                                                                     9
  1     3 1 2   1     2   3   1 2 3 1 2 3 1 2 3          1 2 3

  7
      5 6 4 5 6 4
      8 9   8   7
                      5
                      8
                          6
                          9
                              4 5 6 4 5 6 4 5 6
                              7 8 9 7 8 9 7 8 9     6    4 5 6
                                                         7 8 9   4
      Back to Start           Skip Animation


                                               Helmut Simonis    Visualization Techniques   113
                                            Introduction
                            Visualization by Annotation
                                 Visualization Interface
                                           Conclusions


Propagation Steps (Domain Consistency)
          1 2           1 2 3 1 2 3 1 2 3 1    2 3 1 2 3 1 2               3

      4     5 6
                  8     7
                          5 6
                            9 7
                                5 6
                                  9 7
                                      5 6
                                        9 7
                                               5 6
                                                 9 7
                                                     5 6
                                                       9 7
                                                           5               6
                                                                           9
        3   2     2 3                 2 3      2 3   2 3   2               3
      5 6 4 5 6 4 5 6
      8 9   8     8 9    1 7        4 5 6 4
                                      8 9
                                               5 6 4 5 6 4 5
                                               8 9   8 9   8
                                                                           6
                                                                           9
  1       1     1       1           1     1

  7
      5 6 4 5 6 4 5 6
        9       7   9   7  8
                        4 5 6
                            9
                                    4 5 6 4
                                    7     3 2
                                        9 7
                                               5 6
                                                 9
  1     3 1 2           1 2 3 1 2 3                                1   2   3

  7
      5 6 4 5 6
      8 9   8     6     4 5 6 4 5 6
                        7 8 9 7 8 9   8 2 5                        4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3       1 2 3   1 2 3 1 2 3 1 2 3 1    2 3                 1   2   3

  7     9
      5 6
      8 9
                4 5 6
                7 8 9                     8
                        4 5 6 4 5 6 4 5 6 4
                        7 8 9 7 8 9 7 8 9 7
                                               5 6
                                               8 9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3                     1 2 3 1 2 3              1   2   3   1   2   3

  7     3 7 6
      5 6
      8 9                               9
                              4 5 6 4 5 6
                              7 8 9 7 8 9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
                1 2 3   1 2 3       1 2 3 1    2   3   1   2   3   1   2   3

      2 7     5 4 5 6
                7 8 9
                        4 5 6
                        7 8 9
                                    4 5 6 4
                                    7 8 9 7
                                               5
                                               8
                                                   6
                                                   9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3   1 2 3             1    2   3   1   2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5 6
                7 8 9
                        4 5 6
                        7 8 9
                                          4
                                          7
                                               5
                                               8
                                                   6
                                                   9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3   1 2 3 1 2 3 1 2 3              1   2   3

  7
      5 6 4 5 6 4 5 6
      8 9   8   7 8 9
                        4 5 6 4 5 6 4 5 6
                        7 8 9 7 8 9 7 8 9     6        4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9       4
      Back to Start     Skip Animation


                                         Helmut Simonis                Visualization Techniques   114
                                            Introduction
                            Visualization by Annotation
                                 Visualization Interface
                                           Conclusions


Propagation Steps (Domain Consistency)
          1 2           1 2 3 1 2 3 1 2 3 1    2 3 1 2 3 1 2               3

      4     5 6
                  8     7
                          5 6
                            9 7
                                5 6
                                  9 7
                                      5 6
                                        9 7
                                               5 6
                                                 9 7
                                                     5 6
                                                       9 7
                                                           5               6
                                                                           9
        3   2     2 3                 2 3      2 3   2 3   2               3
      5 6 4 5 6 4 5
      8 9   8       9    1 7        4 5 6 4
                                      8 9
                                               5 6 4 5 6 4 5
                                               8 9   8 9   8
                                                                           6
                                                                           9
  1       1     1       1           1     1

  7
      5 6 4 5 6 4 5
        9           9   7  8
                        4 5 6
                            9
                                    4 5 6 4
                                    7     3 2
                                        9 7
                                               5 6
                                                 9
  1     3 1 2           1 2 3 1 2 3                                1   2   3

  7
      5 6 4 5 6
      8 9   8     6     4 5 6 4 5 6
                        7 8 9 7 8 9   8 2 5                        4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3       1 2 3   1 2 3 1 2 3 1 2 3 1    2 3                 1   2   3

  7     9
      5 6
      8 9
                4 5
                    9                     8
                        4 5 6 4 5 6 4 5 6 4
                        7 8 9 7 8 9 7 8 9 7
                                               5 6
                                               8 9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3                     1 2 3 1 2 3              1   2   3   1   2   3

  7     3 7 6
      5 6
      8 9                               9
                              4 5 6 4 5 6
                              7 8 9 7 8 9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
                1 2 3   1 2 3       1 2 3 1    2   3   1   2   3   1   2   3

      2 7     5 4 5
                    9
                        4 5 6
                        7 8 9
                                    4 5 6 4
                                    7 8 9 7
                                               5
                                               8
                                                   6
                                                   9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3   1 2 3             1    2   3   1   2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5
                    9
                        4 5 6
                        7 8 9
                                          4
                                          7
                                               5
                                               8
                                                   6
                                                   9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3   1 2 3 1 2 3 1 2 3              1   2   3

  7
      5 6 4 5 6 4 5
      8 9   8       9
                        4 5 6 4 5 6 4 5 6
                        7 8 9 7 8 9 7 8 9     6        4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9       4
      Back to Start     Skip Animation


                                         Helmut Simonis                Visualization Techniques   115
                                            Introduction
                            Visualization by Annotation
                                 Visualization Interface
                                           Conclusions


Propagation Steps (Domain Consistency)
          1 2           1 2 3 1 2 3 1 2 3 1    2 3 1 2 3 1 2               3

      4     5 6
                  8     7
                          5 6
                            9 7
                                5 6
                                  9 7
                                      5 6
                                        9 7
                                               5 6
                                                 9 7
                                                     5 6
                                                       9 7
                                                           5               6
                                                                           9
        3   2     2 3                 2 3      2 3   2 3   2               3
      5 6 4 5 6 4 5
      8 9   8       9    1 7        4 5 6 4
                                      8 9
                                               5 6 4 5 6 4 5
                                               8 9   8 9   8
                                                                           6
                                                                           9
  1       1     1       1           1     1

  7
      5 6 4 5 6 4 5
        9           9   7  8
                        4 5 6
                            9
                                    4 5 6 4
                                    7     3 2
                                        9 7
                                               5 6
                                                 9
  1     3 1             1   3 1   3                                1       3

  7     9
          4
                  6     4
                        7
                              4
                            9 7   9   8 2 5                        4
                                                                   7       9
  1     3       1 2 3   1 2 3 1 2 3 1 2 3 1    2 3                 1   2   3

  7     9
      5 6
      8 9
                4 5
                    9                     8
                        4 5 6 4 5 6 4 5 6 4
                        7 8 9 7 8 9 7 8 9 7
                                               5 6
                                               8 9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3                     1 2 3 1 2 3              1   2   3   1   2   3

  7     3 7 6
      5 6
      8 9                               9
                              4 5 6 4 5 6
                              7 8 9 7 8 9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
                1 2 3   1 2 3       1 2 3 1    2   3   1   2   3   1   2   3

      2 7     5 4 5
                    9
                        4 5 6
                        7 8 9
                                    4 5 6 4
                                    7 8 9 7
                                               5
                                               8
                                                   6
                                                   9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3   1 2 3             1    2   3   1   2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5
                    9
                        4 5 6
                        7 8 9
                                          4
                                          7
                                               5
                                               8
                                                   6
                                                   9
                                                       4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3   1 2 3 1 2 3 1 2 3              1   2   3

  7
      5 6 4 5 6 4 5
      8 9   8       9
                        4 5 6 4 5 6 4 5 6
                        7 8 9 7 8 9 7 8 9     6        4
                                                       7
                                                           5
                                                           8
                                                               6
                                                               9       4
      Back to Start     Skip Animation


                                         Helmut Simonis                Visualization Techniques   116
                                              Introduction
                              Visualization by Annotation
                                   Visualization Interface
                                             Conclusions


Propagation Steps (Domain Consistency)
          1 2              2 3 1 2 3 1 2 3     1 2     3 1 2 3 1 2             3

      4     5 6
                  8   7
                           5
                             9 7
                                 5 6
                                   9 7
                                       5 6
                                         9     7
                                                 5     6
                                                       9 7
                                                           5 6
                                                             9 7
                                                                 5             6
                                                                               9
        3   2     2 3                  2 3       2     3   2 3   2             3
      5 6 4 5 6 4 5
      8 9   8       9     1 7        4 5 6
                                       8 9
                                               4 5
                                                 8
                                                       6 4 5 6 4 5
                                                       9   8 9   8
                                                                               6
                                                                               9
  1       1     1                    1         1

  7
      5 6 4 5 6 4 5
        9
                      4
                    9 7
                           5
                            89
                                     4 5 6
                                     7   9  3 24 5
                                               7
                                                       6
                                                       9
  1     3 1                  3 1   3                                   1       3

  7     9
          4
                  6   4
                      7
                               4
                             9 7   9    8 2 5                          4
                                                                       7       9
  1     3       1 2 3      2 3 1 2 3 1 2 3     1 2 3                   1   2   3

  7     9
      5 6
      8 9
                4 5   4
                    9 7
                           5   4 5 6 4 5 6
                           8 9 7 8 9 7 8 9  8  4 5 6
                                               7 8 9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3                      1 2 3 1 2 3                 1   2   3   1   2   3

  7     3 7 6
      5 6
      8 9
                               4 5 6 4 5 6
                               7 8 9 7 8 99                4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
                1 2 3      2 3       1 2 3     1   2   3   1   2   3   1   2   3

      2 7     5 4 5   4
                    9 7
                           5
                           8 9
                                     4 5 6
                                     7 8 9
                                               4
                                               7
                                                   5
                                                   8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3      2 3                 1   2   3   1   2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5   4
                    9 7
                           5
                           8 9
                                               4
                                               7
                                                   5
                                                   8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3      2 3 1 2 3 1 2 3                 1   2   3

  7
      5 6 4 5 6 4 5
      8 9   8
                      4
                    9 7
                           5   4 5 6 4 5 6
                           8 9 7 8 9 7 8 9         6       4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9       4
      Back to Start       Skip Animation


                                           Helmut Simonis                  Visualization Techniques   117
                                              Introduction
                              Visualization by Annotation
                                   Visualization Interface
                                             Conclusions


Propagation Steps (Domain Consistency)
          1 2              2 3 1 2 3 1 2 3     1 2     3 1 2 3 1 2             3

      4     5 6
                  8   7
                           5
                             9 7
                                 5 6
                                   9 7
                                       5 6
                                         9     7
                                                 5     6
                                                       9 7
                                                           5 6
                                                             9 7
                                                                 5             6
                                                                               9
        3   2     2 3                  2 3       2     3   2 3   2             3
      5 6 4 5 6 4 5
      8 9   8       9     1 7        4 5 6
                                       8 9
                                               4 5
                                                 8
                                                       6 4 5 6 4 5
                                                       9   8 9   8
                                                                               6
                                                                               9
  1       1     1                    1         1

  7
      5 6 4 5 6 4 5
        9
                      4
                    9 7
                           5
                            89
                                     4 5 6
                                     7   9  3 24 5
                                               7
                                                       6
                                                       9
  1     3 1                  3 1   3                                   1       3

  7     9
          4
                  6   4
                      7
                               4
                             9 7   9    8 2 5                          4
                                                                       7     9
  1     3       1 2 3      2 3 1 2 3 1 2 3     1 2 3                   1   2 3

  7     9
      5 6       4 5   4
                      7
                           5   4 5 6 4 5 6
                               7     7      8  4 5 6
                                               7
                                                                       4
                                                                       7
                                                                           5 6

  1     3                      1 2 3 1 2 3                 1   2   3   1   2   3

  7     3 7 6
      5 6
      8 9
                               4 5 6 4 5 6
                               7 8 9 7 8 99                4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
                1 2 3      2 3       1 2 3     1   2   3   1   2   3   1   2   3

      2 7     5 4 5   4
                    9 7
                           5
                           8 9
                                     4 5 6
                                     7 8 9
                                               4
                                               7
                                                   5
                                                   8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3      2 3                 1   2   3   1   2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5   4
                    9 7
                           5
                           8 9
                                               4
                                               7
                                                   5
                                                   8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3      2 3 1 2 3 1 2 3                 1   2   3

  7
      5 6 4 5 6 4 5
      8 9   8
                      4
                    9 7
                           5   4 5 6 4 5 6
                           8 9 7 8 9 7 8 9         6       4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9       4
      Back to Start       Skip Animation


                                           Helmut Simonis                  Visualization Techniques   118
                                              Introduction
                              Visualization by Annotation
                                   Visualization Interface
                                             Conclusions


Propagation Steps (Domain Consistency)
          1 2              2 3       2 3 1 2 3   1 2   3 1 2 3 1 2             3

      4     5 6
                  8   7
                           5
                             9
                                       6
                                       9 7
                                           5 6
                                             9   7
                                                   5   6
                                                       9 7
                                                           5 6
                                                             9 7
                                                                 5             6
                                                                               9
        3   2     2 3                      2 3     2   3   2 3   2             3
      5 6 4 5 6 4 5
      8 9   8       9     1 7            4 5 6
                                           8 9
                                                 4 5
                                                   8
                                                       6 4 5 6 4 5
                                                       9   8 9   8
                                                                               6
                                                                               9
  1       1     1                        1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7     89
                                         4 5 6
                                         7   93 24 5
                                                 7
                                                       6
                                                       9
  1     3 1                  3         3                               1       3

  7     9
          4
                  6   4
                      7      9
                                 4
                                   9      8 2 5                        4
                                                                       7     9
  1     3       1 2 3   2    3   2 3 1 2 3 1 2         3               1   2 3

  7     9
      5 6       4 5   4 5
                      7
                               4   6 4 5
                                     7
                                         6 4 5
                                           7  8        6               4
                                                                       7
                                                                           5 6

  1     3                        2 3 1 2 3                 1   2   3   1   2   3

  7     3 7 6
      5 6
      8 9
                               4   6 4 5
                                   9 7 8
                                         6
                                         9  9              4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
                1 2 3   2    3       1 2 3 1 2         3   1   2   3   1   2   3

      2 7     5 4 5   4 5
                    9 7 8    9
                                     4 5
                                     7 8
                                         6 4 5
                                         9 7 8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3   2    3             1 2         3   1   2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5   4 5
                    9 7 8    9
                                           4 5
                                           7 8
                                                       6
                                                       9
                                                           4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3   2    3   2 3 1 2 3                 1   2   3

  7
      5 6 4 5 6 4 5
      8 9   8
                      4 5
                    9 7 8    9
                               4   6 4 5 6
                                   9 7 8 9        6        4
                                                           7
                                                               5
                                                               8
                                                                   6
                                                                   9       4
      Back to Start       Skip Animation


                                           Helmut Simonis                  Visualization Techniques   119
                                                Introduction
                                Visualization by Annotation
                                     Visualization Interface
                                               Conclusions


Propagation Steps (Domain Consistency)
          1 2                2 3       2 3 1 2 3   1 2   3 1 2 3 1 2           3

      4     5 6
                  8     7
                             5
                               9
                                         6
                                         9 7
                                             5 6
                                               9   7
                                                     5   6
                                                         9 7
                                                             5 6
                                                               9 7
                                                                   5           6
                                                                               9
        3   2     2 3                        2 3     2   3   2 3   2           3
      5 6 4 5 6 4 5
      8 9   8       9       1 7            4 5 6
                                             8 9
                                                   4 5
                                                     8
                                                         6 4 5 6 4 5
                                                         9   8 9   8
                                                                               6
                                                                               9
  1       1     1                          1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7       89
                                           4 5 6
                                           7   93 24 5
                                                   7
                                                         6
                                                         9
  1     3 1                    3         3                             1       3

  7     9
          4
                  6   4
                      7        9  9
                                   4
                                            8 2 5                      4
                                                                       7     9
  1     3       1 2 3   2      32 3 1 2        3 1 2 3                 1   2 3

  7     9
      5 6       4 5   4 5
                      7
                              4   6 4 5
                                    7           8
                                               6 4 5 6
                                                 7
                                                                       4
                                                                       7
                                                                           5 6

  1                             2   1 2                      1 2       1   2
      5
      8 3 7 6                 4     4 5
                                      8       9              4 5
                                                               8
                                                                       4   5
                                                                           8
                1 2 3     2 3       1 2        3 1 2 3       1 2   3   1   2   3

      2 7     5 4 5
                    9
                        4 5
                        7 8 9
                                    4 5
                                    7 8
                                               6 4 5 6
                                               9 7 8 9
                                                             4 5
                                                             7 8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3     2 3                    1 2 3       1 2   3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5
                    9
                        4 5
                        7 8 9
                                                 4 5 6
                                                 7 8 9
                                                             4 5
                                                             7 8
                                                                   6
                                                                   9
                                                                       4
                                                                       7
                                                                           5
                                                                           8
                                                                               6
                                                                               9
  1     3 1 2   1 2 3     2 3   2 3 1 2        3             1 2   3

  7
      5 6 4 5 6 4 5
      8 9   8       9
                        4 5
                        7 8 9
                              4   6 4 5
                                  9 7 8
                                               6
                                               9    6        4 5
                                                             7 8
                                                                   6
                                                                   9       4
      Back to Start         Skip Animation


                                             Helmut Simonis                Visualization Techniques   120
                                               Introduction
                               Visualization by Annotation
                                    Visualization Interface
                                              Conclusions


Propagation Steps (Domain Consistency)
          1 2              2 3         2 3 1 2 3   1 2   3 1 2 3 1 2       3

      4     5 6
                  8   7
                           5
                             9
                                         6
                                         9 7
                                             5 6
                                               9   7
                                                     5   6
                                                         9 7
                                                             5 6
                                                               9 7
                                                                   5       6
                                                                           9
        3   2     2 3                        2 3     2   3   2 3   2       3
      5 6 4 5 6 4 5
      8 9   8       9     1 7                5 6
                                               9
                                                   4 5
                                                     8
                                                         6 4 5 6 4 5
                                                         9   8 9   8
                                                                           6
                                                                           9
  1       1     1                          1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7     8  9           7
                                             5 6
                                               93 24 5
                                                   7
                                                         6
                                                         9
  1     3 1                    3         3                         1       3

  7     9
          4
                  6   4
                      7        9
                                   4
                                       9    8 2 5                  4
                                                                   7     9
  1     3       1 2 3   2      3     2 3 1 2 3 1 2 3               1   2 3

  7     9
      5 6       4 5   4 5
                      7
                                   4   6
                                         7      8
                                           5 6 4 5 6
                                               7
                                                                   4
                                                                   7
                                                                       5 6

  1                                  2   1 2         1 2           1   2
      5
      8 3 7 6                      4       5
                                              9      4 5
                                                       8
                                                                   4   5
                                                                       8
                1 2 3      2   3         1 2 3 1 2 3 1 2       3   1   2   3

      2 7     5 4 5   4
                    9 7
                           5
                           8   9         7
                                           5 6 4 5 6 4 5
                                             9 7 8 9 7 8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3      2   3               1 2 3 1 2       3   1   2   3

  7   8 9   8 1 4
      5 6 4 5 6 4 5   4
                    9 7
                           5
                           8   9
                                               4 5 6 4 5
                                               7 8 9 7 8
                                                               6
                                                               9
                                                                   4
                                                                   7
                                                                       5
                                                                       8
                                                                           6
                                                                           9
  1     3 1 2   1 2 3      2   3     2 3 1 2 3       1 2       3

  7
      5 6 4 5 6 4 5
      8 9   8
                      4
                    9 7
                           5
                           8   9
                                   4   6
                                       9 7
                                           5 6
                                             9      64 5
                                                     7 8
                                                               6
                                                               9       4
      Back to Start       Skip Animation


                                             Helmut Simonis            Visualization Techniques   121
                                                       Introduction
                                       Visualization by Annotation
                                            Visualization Interface
                                                      Conclusions


Propagation Steps (Domain Consistency)
          1 2                      2 3         2 3 1 2 3   1 2   3 1 2 3 1 2       3

      4     5 6
                      8       7
                                   5
                                     9
                                                 6
                                                 9 7
                                                     5 6
                                                       9   7
                                                             5   6
                                                                 9 7
                                                                     5 6
                                                                       9 7
                                                                           5       6
                                                                                   9
        3   2     2 3                                2 3     2   3   2 3   2       3
      5 6 4 5 6 4 5
      8 9   8       9             1 7                5 6
                                                       9
                                                           4 5
                                                             8
                                                                 6 4 5 6 4 5
                                                                 9   8 9   8
                                                                                   6
                                                                                   9
  1       1     1                                  1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7             8  9           7
                                                     5 6
                                                       93 24 5
                                                           7
                                                                 6
                                                                 9
  1     3 1                            3         3                         1       3

  7     9
          4
                      6
                      4
                      7                9
                                           4
                                               9    8 2 5                  4
                                                                           7     9
  1     3       1 2 3   2              3     2 3 1 2 3 1 2 3               1   2 3

  7     9
      5 6       4 5   4 5
                      7
                                           4   6
                                                 7      8
                                                   5 6 4 5 6
                                                       7
                                                                           4
                                                                           7
                                                                               5 6

  1                                          2   1 2         1 2           1   2
      5
      8 3 7 6                              4       5
                                                      9      4 5
                                                               8
                                                                           4   5
                                                                               8
                  1       3            3         1   3 1   3 1         3   1       3

      2 7     5   4
                        9
                              4
                                   8   9
                                                     6 4
                                                     9
                                                           6 4
                                                         8 9   8
                                                                       6
                                                                       9
                                                                           4
                                                                             8
                                                                                   6
                                                                                   9
  1   3   1 2     1   2 3          2   3               1 2 3 1 2       3   1 2     3
    5 6
  7 8 9     8 1 4
          4 5 6   4   5
                        9
                              4
                              7
                                   5
                                   8   9
                                                       4 5 6 4 5
                                                       7 8 9 7 8
                                                                       6
                                                                       9
                                                                           4 5
                                                                           7 8
                                                                                   6
                                                                                   9
  1   3   1 2     1   2 3          2   3     2 3 1 2 3       1 2       3
    5 6
  7 8 9
          4 5 6
            8
                  4   5
                        9
                              4
                              7
                                   5
                                   8   9
                                           4   6
                                               9 7
                                                   5 6
                                                     9      64 5
                                                             7 8
                                                                       6
                                                                       9       4
      Back to Start               Skip Animation


                                                     Helmut Simonis            Visualization Techniques   122
                                                       Introduction
                                       Visualization by Annotation
                                            Visualization Interface
                                                      Conclusions


Propagation Steps (Domain Consistency)
          1 2                      2 3         2 3 1 2 3   1   3 1 2   3 1 2 3

      4     5 6
                      8       7
                                   5
                                     9
                                                 6
                                                 9 7
                                                     5 6
                                                       9   7
                                                               5
                                                                 7
                                                                   5   6
                                                                       9 7
                                                                           5 6
                                                                             9
        3   2     2 3                                2 3       3   2   3   2 3
      5 6 4 5 6 4 5
      8 9   8       9             1 7                5 6
                                                       9
                                                           4 5
                                                             8
                                                                 4 5
                                                                   8
                                                                       6 4 5 6
                                                                       9   8 9
  1       1     1                                  1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7             8  9           7
                                                     5 6
                                                       93 24 5
                                                           7
  1     3 1                            3         3                         1       3

  7     9
          4
                      6
                      4
                      7                9
                                           4
                                               9    8 2 5                  4
                                                                           7     9
  1     3       1 2 3   2              3     2 3 1 2 3 1   3               1   2 3

  7     9
      5 6       4 5   4 5
                      7
                                           4   6
                                                 7      8
                                                   5 6 4 5
                                                       7
                                                                           4
                                                                           7
                                                                               5 6

  1                                          2   1 2         1 2           1   2
      5
      8 3 7 6                              4       5
                                                      9      4 5
                                                               8
                                                                           4   5
                                                                               8
                  1       3            3         1   3 1   3 1         3   1       3

      2 7     5   4
                        9
                              4
                                   8   9
                                                     6 4
                                                     9   8
                                                             4
                                                               8
                                                                       6
                                                                       9
                                                                           4
                                                                             8
                                                                                   6
                                                                                   9
  1   3   1 2     1   2 3          2   3               1   3 1 2       3   1 2     3
    5 6
  7 8 9       1 4
          4 5 6
            8
                  4   5
                        9
                              4
                              7
                                   5
                                   8   9
                                                       4 5
                                                       7 8
                                                             4 5
                                                             7 8
                                                                       6
                                                                       9
                                                                           4 5
                                                                           7 8
                                                                                   6
                                                                                   9
  1   3   1 2     1   2 3          2   3     2 3 1 2 3       1 2       3
    5 6
  7 8 9
          4 5 6
            8
                  4   5
                        9
                              4
                              7
                                   5
                                   8   9
                                           4   6
                                               9 7
                                                   5 6
                                                     9         6
                                                             4 5
                                                             7 8
                                                                       6
                                                                       9       4
      Back to Start               Skip Animation


                                                     Helmut Simonis            Visualization Techniques   123
                                                      Introduction
                                      Visualization by Annotation
                                           Visualization Interface
                                                     Conclusions


Propagation Steps (Domain Consistency)
          1 2                      2 3       2 3 1 2 3   1   3 1 2   3 1 2 3

      4     5 6
                      8       7
                                   5
                                     9
                                               6
                                               9 7
                                                   5 6
                                                     9   7
                                                             5
                                                               7
                                                                 5   6
                                                                     9 7
                                                                         5 6
                                                                           9
        3   2     2 3                              2 3       3   2   3   2 3
      5 6 4 5 6 4 5
      8 9   8       9             1 7              5 6
                                                     9
                                                         4 5
                                                           8
                                                               4 5
                                                                 8
                                                                     6 4 5 6
                                                                     9   8 9
  1       1     1                                1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7             89           7
                                                   5 6
                                                     93 24 5
                                                         7
  1     3 1                          3         3                       1       3

  7     9
          4
                      6
                      4
                      7              9
                                         4
                                             9    8 2 5                4
                                                                       7     9
  1     3       1 2 3   2            3     2 3 1 2 3 1   3             1   2 3

  7     9
      5 6       4 5   4 5
                      7
                                         4   6
                                               7      8
                                                 5 6 4 5
                                                     7
                                                                       4
                                                                       7
                                                                           5 6

  1                                        2   1 2         1 2         1   2
      5
      8 3 7 6                            4       5
                                                    9      4 5
                                                             8
                                                                       4   5
                                                                           8
                  1     3 3                    1   3 1   3 1         3 1   3

      2 7     5   4
                  9
                    4
                      8 9
                                                   6 4
                                                   9   8
                                                           4
                                                             8
                                                                     6 4
                                                                     9
                                                                           6
                                                                         8 9
      3   2     2 3   2 3                                3   2       3   2 3
    5 6
  7 8 9
          5 6
          8   1 4
                5     5
                  9 7 8 9
                                                       5
                                                     7 8
                                                             5
                                                           7 8
                                                                     6   5 6
                                                                     9 7 8 9
  1   3 1 2   1 2 3   2 3                  2 3 1 2 3       1 2       3
    5 6 4 5 6 4 5
  7 8 9   8
                    4 5
                  9 7 8 9
                                         4   6
                                             9 7
                                                 5 6
                                                   9         6
                                                           4 5
                                                           7 8
                                                                     6
                                                                     9     4
      Back to Start               Skip Animation


                                                   Helmut Simonis          Visualization Techniques   124
                                                      Introduction
                                      Visualization by Annotation
                                           Visualization Interface
                                                     Conclusions


Propagation Steps (Domain Consistency)
          1 2                      2 3       2 3 1 2 3   1           1 2 3
                                                                 3 1 2

      4     5 6
                      8       7
                                   5
                                     9
                                               6
                                               9 7
                                                   5 6
                                                     9   7
                                                             5     6
                                                                   9 7
                                                                   7
                                                                       5 6
                                                                         9
        3   2     2 3                              2 3       3   2     2 3
      5 6 4 5 6 4 5
      8 9   8       9             1 7              5 6
                                                     9
                                                         4 5
                                                           8
                                                               4   6 4 5 6
                                                                   9   8 9
  1       1     1                                1       1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7             89           7
                                                   5 6
                                                     93 24 5
                                                         7
  1     3 1                          3         3                     1   3

  7     9
          4
                      6
                      4
                      7              9
                                         4
                                             9    8 2 5              4
                                                                     7   9
  1     3       1 2 3   2            3     2 3 1 2 3     1   3       1 2 3

  7     9
      5 6       4 5   4 5
                      7
                                         4   6
                                               7
                                                 5 6
                                                      8  4 5
                                                         7
                                                                     4 5 6
                                                                     7
  1                                        2   1 2             1 2   1 2
      5
      8 3 7 6                            4       5
                                                    9          4     4 5
                                                                       8
                  1     3 3     1   3                    1   3 1     1   3

      2 7     5   4
                  9
                    4
                      8 9
                                    6
                                    9
                                                         4
                                                           8
                                                               4   6 4
                                                                   9
                                                                         6
                                                                       8 9
      3   2     2 3   2 3                                    3   2     2 3
    5 6
  7 8 9
          5 6
          8   1 4
                5     5
                  9 7 8 9
                                                           5
                                                         7 8   7
                                                                   6   5 6
                                                                   9 7 8 9
  1   3 1 2   1 2 3   2 3   2 3 1 2 3                          1 2
    5 6 4 5 6 4 5
  7 8 9   8
                    4 5
                  9 7 8 9
                          4   6
                              9 7
                                  5 6
                                    9                        6 4
                                                               7
                                                                   6
                                                                   9     4
      Back to Start               Skip Animation


                                                   Helmut Simonis        Visualization Techniques   125
                                                        Introduction
                                        Visualization by Annotation
                                             Visualization Interface
                                                       Conclusions


Propagation Steps (Domain Consistency)
            1 2                      2 3       2 3 1 2 3     1           1 2 3
                                                                     3 1 2

      4       5 6
                        8       7
                                     5
                                       9
                                                 6
                                                 9 7
                                                     5 6
                                                       9     7
                                                                 5     6
                                                                       9 7
                                                                       7
                                                                           5 6
                                                                             9
        3   2     2 3                                2 3         3   2     2 3
      5 6 4 5 6 4 5
      8 9   8       9               1 7              5 6
                                                       9
                                                             4 5
                                                               8
                                                                   4   6 4 5 6
                                                                       9   8 9
  1       1     1                                  1         1

  7
      5 6 4 5 6 4 5
        9
                      4 5
                    9 7               89           7
                                                     5 6
                                                       9   3 2
                                                             4 5
                                                             7
  1     3 1                            3         3                       1   3

  7     9
          4           4
                      7 6              9
                                           4
                                               9       8 2 5             4
                                                                         7   9
  1     3       1 2 3   2              3     2 3 1 2 3       1   3       1 2 3

  7     9
      5 6       4 5   4 5
                      7
                                           4   6
                                                 7
                                                   5 6
                                                           8 4 5
                                                             7
                                                                         4 5 6
                                                                         7
  1                                          2   1 2               1 2   1 2
      5
      8 3 7 6                              4       5
                                                         9         4     4 5
                                                                           8
                    1       3
                            3                      1     3   1   3 1     1   3

      2 7     5     4
                      9
                        4
                          8 9
                                                         6
                                                         9
                                                             4
                                                               8
                                                                   4   6 4
                                                                       9
                                                                             6
                                                                           8 9
          3   2     2 3   2 3                                    3   2     2 3
    5
  7 8
          6
          9   1 4
              5 6
              8
                    5     5
                      9 7 8 9
                                                               5
                                                             7 8   7
                                                                       6   5 6
                                                                       9 7 8 9
  1       3 1 2   1 2 3   2 3                  2 3 1 2 3           1 2
    5
  7 8     9
              5
              8
                    5     5
                      9 7 8 9                    9 7
                                                     5
                                                       9         6     7     9   4
      Back to Start                 Skip Animation


                                                       Helmut Simonis            Visualization Techniques   126
                                              Introduction
                              Visualization by Annotation
                                   Visualization Interface
                                             Conclusions


Propagation Steps (Domain Consistency)
          1 2              2 3    2 3 1 2 3    1           1
                                                       3 1 2   3

      4     5 6
                  8   7
                           5
                             9
                                    6
                                    9 7
                                        5 6
                                          9    7
                                                   5     6
                                                         9 7
                                                         7
                                                             5 6
                                                               9
        3   2     2 3                   2 3        3   2       3
      5 6 4 5 6 4 5
      8 9   8       9     1 7           5 6
                                          9
                                               4 5
                                                 8
                                                     4   6
                                                         9
                                                             5 6
                                                             8 9
          1     1                     1        1

      7   4 5 6 4 5   4 5
                    9 7   9 8         7
                                        5 6
                                          9 3 24 5
                                               7
  1     3                 3         3                      1   3

  7     4 6
        9
                      4
                      7   9
                            4
                                9       8 2 5                  7     9
  1     3       1 2 3   2 3   2 3 1        2 3 1   3           1     3

  7     9
      5 6       4 5   4 5
                      7
                            4   6
                                  7         8
                                           5 6 4 5
                                               7               7
                                                                   5 6

  1                           2   1        2         1 2       1
      5
      8 3 7 6               4
                                          95         4       5
                                                             8
                1   3     3       1          3 1   3 1     1   3

      2 7     5 4
                    9
                      4
                        8 9
                                             6 4
                                             9   8
                                                     4   6
                                                         9
                                                               6
                                                             8 9
        3   2     2 3   2 3                        3   2       3

  7
      5 6
      8 9   8 1 4
            5 6   5     5
                    9 7 8 9
                                                 5
                                               7 8   7
                                                         6   5 6
                                                         9 7 8 9
  1     3 1 2   1 2 3   2 3   2 3 1        2 3       1 2

  7
      5
      8 9
            5
            8
                  5     5
                    9 7 8 9     9 7
                                           5
                                             9     6 7   9         4
      Back to Start       Skip Animation


                                           Helmut Simonis          Visualization Techniques   127
                                                            Introduction
                                            Visualization by Annotation
                                                 Visualization Interface
                                                           Conclusions


Propagation Steps (Domain Consistency)
              1 2                        2 3    2 3 1 2 3    1           1
                                                                     3 1 2   3

      4         5 6
                            8       7
                                         5
                                           9
                                                  6
                                                  9 7
                                                      5 6
                                                        9    7
                                                                 5     6
                                                                       9 7
                                                                       7
                                                                           5 6
                                                                             9
        3         2         2 3                       2 3        3   2       3
      5 6
        9
                  5 6       5
                              9         1 7           5 6
                                                        9
                                                             4 5
                                                               8
                                                                   4   6
                                                                       9
                                                                           5 6
                                                                           8 9
              1         1                           1        1

      7           5 6       5
                                9       4 8           5 6
                                                        9    3 2
                                                             4 5

  1       3                                3      3                          1       3

      9 4 6                       9 7   9                8 2 5               7     9
  1   3                 1 2 3   2 3   2 3 1              2 3 1   3           1     3
    5 6
        9               4 5   4 5
                              7
                                    4   6
                                          7                  8
                                                         5 6 4 5
                                                             7               7
                                                                                 5 6

  1                                   2   1              2         1 2       1
      5
      8 3 7 6                       4                    5
                                                           9       4    5
                                                                        8
                        1       3          3         1  3 1   3 1     1   3

      2 7     5       9
                        4
                        4
                          8 9
                                                        6 4
                                                        9   8
                                                                4   6
                                                                    9
                                                                          6
                                                                        8 9
          3   2     2 3   2 3                                 3   2       3
      5
      8
          6
          9   1 4
              5 6
              8
                    5     5
                      9 7 8 9
                                                            5
                                                          7 8   7
                                                                    6   5 6
                                                                    9 7 8 9
  1       3 1 2   1 2 3   2 3                   2 3 1 2 3       1 2
      5
      8   9
              5
              8
                    5     5
                      9 7 8 9                     9 7
                                                      5
                                                        9       76  9            4
      Back to Start                     Skip Animation


                                                         Helmut Simonis          Visualization Techniques   128
                                                            Introduction
                                            Visualization by Annotation
                                                 Visualization Interface
                                                           Conclusions


Propagation Steps (Domain Consistency)
              1 2                        2 3    2 3       2 3 1   3 1 2   1   3

      4         5 6
                            8            5
                                           9
                                                  6
                                                  9
                                                          5 6
                                                            9 7
                                                                5
                                                                    7
                                                                        6
                                                                        9 7
                                                                            5 6
                                                                              9
        3         2         2 3                           2 3     3   2       3
      5 6
        9
                  5 6       5
                              9         1 7               5 6 4 5
                                                            9   8
                                                                    4   6
                                                                        9
                                                                            5 6
                                                                            8 9
              1         1                                     1

      7           5 6       5
                                9       4 8               5 6
                                                            9 3 2
                                                                5

  1       3                                3      3                       1   3

        4 6
        9                           7   9     9           8 2 5            7     9
  1     3               1 2 3         2 3   2 3 1 2 3 1   3                1     3

        9
      5 6               4 5
                                    7
                                      5   4   6
                                                7
                                                  5 6 4 5
                                                      7       8            7
                                                                               5 6

  1                                         2   1 2         1 2            1
      5
      8 3 7 6                             4       5
                                                            9
                                                            4           5
                                                                        8
                        1       3          3          1 3 1   3 1     1   3

      2 7     5   9
                        4
                      8 9
                                                        6 4
                                                        9   8
                                                                4   6
                                                                    9
                                                                          6
                                                                        8 9
      3   2     2 3   2 3                                     3   2       3
    5 6
    8 9
          5 6
          8   1 4
                5     5
                  9 7 8 9
                                                            5
                                                          7 8   7
                                                                    6   5 6
                                                                    9 7 8 9
  1   3 1 2   1 2 3   2 3                       2 3 1 2 3       1 2
    5
    8 9
          5
          8
                5     5
                  9 7 8 9                         9 7
                                                      5
                                                        9      67   9          4
      Back to Start                     Skip Animation


                                                          Helmut Simonis       Visualization Techniques   129
                                                        Introduction
                                        Visualization by Annotation
                                             Visualization Interface
                                                       Conclusions


Propagation Steps (Domain Consistency)
          1 2                        2 3    2 3       2 3 1     1        1

   4        5 6
                        8            5
                                       9
                                              6
                                              9
                                                      5 6
                                                        9 7
                                                            5
                                                                7
                                                                       6
                                                                       9 7
                                                                           5 6
                                                                             9
      3       2         2 3                           2 3
    5 6
      9
              5 6       5
                          9         1 7               5 6 4 5
                                                        9   8
                                                                4      6
                                                                       9
                                                                               5 6
                                                                               8 9
          1         1                                     1

   7          5 6       5
                            9       4 8               5 6
                                                        9 3 2
                                                            5

                                       3      3                            1       3

   1          4         6       7   9     9           8 2 5                7     9
                                  2 3   2 3 1 2 3 1   3                    1     3

   5          9         2       7
                                  5   4   6
                                            7
                                              5 6 4 5
                                                  7       8                7
                                                                               5 6

                                        2   1 2         1 2                1

   8          3         7 6           4       5
                                                        9
                                                        4           5
                                                                    8
                                       3          1 3 1   3 1     1   3

   2          7         4
                      8 9   5                       6 4
                                                    9   8
                                                            4   6
                                                                9
                                                                      6
                                                                    8 9
      3   2     2 3   2 3                                 3   2       3
    5 6
    8 9
          5 6
          8
                5     5
                  9 7 8 9   1 4                         5
                                                      7 8   7
                                                                6   5 6
                                                                9 7 8 9
  1   3 1 2   1 2 3   2 3                   2 3 1 2 3       1 2
    5
    8 9
          5
          8
                5     5
                  9 7 8 9                     9 7
                                                  5
                                                    9      67   9              4
    Back to Start                   Skip Animation


                                                      Helmut Simonis           Visualization Techniques   130
                                                   Introduction
                                   Visualization by Annotation
                                        Visualization Interface
                                                  Conclusions


Propagation Steps (Domain Consistency)
                                                              1         1

   4 2         8 5                    6 3 1                   7
                                                                      6
                                                                      9 7
                                                                          5 6
                                                                            9
     3                 3

     5
     6
     9           1 5
                       9              7 2 4 6                                 8
   7 6         1 4                    8 9 5 3                                 2
                                  3      3                                        3

   1 4         6           7      9     8 2 5
                                         9                                7       9
                                  3                 1     3

   5 9         2           7          4 1   8       4
                                                    7                         6
   8 3         7 6                    2 5 9 4                                 1
                                  3                                       1     3

   2 7         4                8 9   5 6 8 1                                   6
                                                                              8 9
                       3                                  3       2

   6 8           2 5
                       9              1 4             5
                                                    7 8       7
                                                                      6
                                                                      9       5
     3                                 2 3

     1
     9         5 8                      7 6 2
                                         9                                    4
   Back to Start               Skip Animation


                                                Helmut Simonis                Visualization Techniques   131
                                               Introduction
                               Visualization by Annotation
                                    Visualization Interface
                                              Conclusions


Propagation Steps (Domain Consistency)

   4 2         8 5                6 3 1                 7     9 7         9
     3             3

     5
     9           1 9              7 2 4 6                             8
   7 6         1 4                8 9 5 3                             2
                              3      3                                    3

   1 4         6       7      9     8 2 5
                                     9                            7       9
                              3                     3

   5 9         2       7          4 1   8       7                     6
   8 3         7 6                2 5 9 4                             1
                              3                                           3

   2 7         4              9   5 6 8 1                                 9
                   3                                3

   6 8           2 9              1 4           7       7     9       5
     3                               3

     1
     9         5 8                  7 6 2
                                     9                                4
   Back to Start           Skip Animation


                                            Helmut Simonis            Visualization Techniques   132
                                               Introduction
                               Visualization by Annotation
                                    Visualization Interface
                                              Conclusions


Propagation Steps (Domain Consistency)

   4 2         8 5                6 3 1                 7     9 7         9
     3             3

     5
     9           1 9              7 2 4 6                             8
   7 6         1 4                8 9 5 3                             2
                              3      3                                    3

   1 4         6       7      9     8 2 5
                                     9                            7
                              3                     3

   5 9         2       7          4 1   8       7                     6
   8 3         7 6                2 5 9 4                             1
                              3                                           3

   2 7         4              9   5 6 8 1                                 9
                   3                                3

   6 8           2 9              1 4           7       7     9       5
     3                               3

     1
     9         5 8                  7 6 2
                                     9                                4
   Back to Start           Skip Animation


                                            Helmut Simonis            Visualization Techniques   133
                                               Introduction
                               Visualization by Annotation
                                    Visualization Interface
                                              Conclusions


Propagation Steps (Domain Consistency)

   4 2         8 5                6 3 1                 7     9 7         9
     3             3

     5
     9           1 9              7 2 4 6                             8
   7 6         1 4                8 9 5 3                             2
                              3      3                                    3

   1 4         6       7      9     8 2 5
                                     9                            7
                              3                     3

   5 9         2       7          4 1   8       7                     6
   8 3         7 6                2 5 9 4                             1
                              3                                           3

   2 7         4              9   5 6 8 1                                 9
                   3                                3

   6 8           2 9              1 4           7       7     9       5
     3                               3

     1
     9         5 8                  7 6 2
                                     9                                4
   Back to Start           Skip Animation


                                            Helmut Simonis            Visualization Techniques   134
                                               Introduction
                               Visualization by Annotation
                                    Visualization Interface
                                              Conclusions


Propagation Steps (Domain Consistency)

   4 2         8 5                6 3 1                 7     9 7         9
     3             3

     5
     9           1 9              7 2 4 6                             8
   7 6         1 4                8 9 5 3                             2
                              3      3                                    3

   1 4         6       7      9     8 2 5
                                     9                            7
                              3                     3

   5 9         2       7          4 1   8       7                     6
   8 3         7 6                2 5 9 4                             1
                              3                                           3

   2 7         4              9   5 6 8 1                                 9
                   3                                3

   6 8           2 9              1 4           7       7     9       5
     3                               3

     1
     9         5 8                  7 6 2
                                     9                                4
   Back to Start           Skip Animation


                                            Helmut Simonis            Visualization Techniques   135
                                           Introduction
                           Visualization by Annotation
                                Visualization Interface
                                          Conclusions


Propagation Steps (Domain Consistency)

   4 2         8 5             6 3 1                7     9 7         9
     3             3

     5
     9           1 9           7 2 4 6                            8
   7 6         1 4             8 9 5 3                            2
                           3     3                                    3

   1 4         6       7   9     8 2 5
                                 9                            7
                           3                    3

   5 9         2       7       4 1   8     7                      6
   8 3         7 6             2 5 9 4                            1
                           3                                          3

   2 7         4           9   5 6 8 1                                9
                   3                            3

   6 8           2 9           1 4         7        7     9       5
     3                           3

     1
     9         5 8               7 6 2
                                 9                                4
   Back to Start


                                      Helmut Simonis              Visualization Techniques   136
                                  Introduction
                  Visualization by Annotation
                       Visualization Interface
                                 Conclusions


After Setup (Domain Consistency)

   4 2   8 5          6 3 1                7     9 7         9
    3     3

    95    91          7 2 4 6                            8
   7 6   1 4          8 9 5 3                            2
                  3     3                                    3

   1 4   6    7   9     8 2 5
                        9                            7
                  3                    3

   5 9   2    7       4 1   8     7                      6
   8 3   7 6          2 5 9 4                            1
                  3                                          3

   2 7   4        9   5 6 8 1                                9
          3                            3

   6 8    92          1 4         7        7     9       5
    3                   3

    91   5 8            7 6 2
                        9                                4

                             Helmut Simonis              Visualization Techniques   137
                                                                                         Introduction
                                                                         Visualization by Annotation
                                                                              Visualization Interface
                                                                                        Conclusions


Comparison



  Forward Checking                                                                         Bounds Consistency                                                                        Domain Consistency
               1 2                       2 3       3       2 3 1         1                             1 2                                   2 3 1             1

       4         5 6
                             8           5
                                           9
                                                   6
                                                   9
                                                             6
                                                             9 7
                                                                 5
                                                                         7
                                                                             6
                                                                             9 7
                                                                                 5 6
                                                                                   9           4                 8 5                     6         7           7       9 7       9    4 2   8 5          6 3 1       7   9 7         9
           3       2             3                         2 3                                     3     2           3                       2 3                                       3     3
           6
           9
                   5 6       5
                                 9       1 7                 6 4 5
                                                             9   8
                                                                             6
                                                                             9
                                                                                     5 6
                                                                                     8 9           9
                                                                                                         5
                                                                                                                   1 9                   7         4 5
                                                                                                                                                     8
                                                                                                                                                                       6
                                                                                                                                                                       9
                                                                                                                                                                               5
                                                                                                                                                                               8 9     95    91          7 2 4 6                 8
               1         1                                     1                                             1                                     1

   7
           6
           9
                   5 6       5
                               3 2
                                 9
                                     4 5
                                           8
                                           9
                                                             6 4 5
                                                             9 7                               7         6       5
                                                                                                                   4                     8 9   3 2   5
                                                                                                                                                                                      7 6   1 4          8 9 5 3                 2
                                           3       3                                   3                                         3       3                                       3                   3   3                           3

       1           4 6     8 2 5     7     9       9                             7             1         4       6       7       9       9 8 2 5                           7          1 4   6    7   9   9 8 2 5             7
                                           3       3 1       3       3                 3                                         3       3                 3                                         3           3

       5           9 2         8     4
                                     7
                                               4
                                                       7         7               7
                                                                                       6
                                                                                               5         9       2       7
                                                                                                                                     4
                                                                                                                                           1   8 6 7                                  5 9   2    7       4 1 7 8                 6
       8           3 7 6 2 5 9 4 1                                                             8         3       7 6                     2 5 9 4 1                                    8 3   7 6          2 5 9 4                 1
                         1       3         3                 3 1   3 1         3                                                 3                 1       3 1                   3                   3                               3

       2           7   9 5
                         4
                                         8 9
                                                             6
                                                             9   8       9   8 9               2         7       4           8 9         5 6           8               9   8 9        2 7   4        9   5 6 8 1                     9
           3           3                 2 3                       3   2       3                                     3       2 3                           3       2         3               3                   3
           6
           9
               5 6
               8
                     5
                         1 4
                       9 7               8 9
                                                                 5
                                                               7 8   7
                                                                             5
                                                                         9 7 8 9               6         5
                                                                                                         8           9       8 9         1 4         5
                                                                                                                                                   7 8         7
                                                                                                                                                                           5
                                                                                                                                                                       9 7 8 9        6 8    92          1 4 7       7   9       5
           3 1     1   3                 2 3       3       2 3       1 2                           3 1       1               2           3                     1 2                     3                 3

           9
               5
               8
                     5
                       9 7   6   4       8 9       9 7       9           7   9                     9
                                                                                                         5
                                                                                                         8
                                                                                                                 5
                                                                                                                             8           9 7 6   4                                     91   5 8          9 7 6 2                 4




                                                                                           Helmut Simonis                                    Visualization Techniques                                                                    138
                              Introduction
              Visualization by Annotation
                   Visualization Interface
                             Conclusions


Instrumented indomain
  tree_indomain_generic(Term,Handle,Handle,Type):-
    Handle = visualization{ignore_fixed:IgnoreFixed,
                           var_arg:VarArg,
                           name_arg:NameArg,
                           focus_arg:FocusArg},
    arg(VarArg,Term,X),
    ((integer(X),IgnoreFixed = yes) ->
        true
    ;
        arg(NameArg,Term,Name),
        arg(FocusArg,Term,Focus),
        get_domain_as_list(X,L),
        get_domain_size(X,Size),
        reorganize_domain(X,L,Type,K),
        try_value(Handle,X,K,Name,Size,Focus)
    ).
                         Helmut Simonis      Visualization Techniques   139
                             Introduction
             Visualization by Annotation
                  Visualization Interface
                            Conclusions


Instrumented indomain

  try_value(Handle,X,[V|_],Name,Size,Focus):-
    ((X = V, true) ->
        try(Handle,Name,Size,V),
        focus_option(Focus,FocusOption),
        draw_visualization(Handle,FocusOption)
    ;
        failure(Handle,Name,Size,V),
        fail_option(Focus,V,FailOption),
        draw_visualization(Handle,FailOption),
        fail
    ).
  try_value(Handle,X,[_|R],Name,Size,Focus):-
    try_value(Handle,X,R,Name,Size,Focus).

                        Helmut Simonis      Visualization Techniques   140
                                     Introduction
                     Visualization by Annotation    TreeLog Format
                          Visualization Interface   VisualizerLog Format
                                    Conclusions


Outline


  1   Introduction

  2   Visualization by Annotation

  3   Visualization Interface
         TreeLog Format
         VisualizerLog Format

  4   Conclusions



                                Helmut Simonis      Visualization Techniques   141
                                 Introduction
                 Visualization by Annotation       TreeLog Format
                      Visualization Interface      VisualizerLog Format
                                Conclusions


Architecture (Current)
           Program + Annotation

                   ECLiPSe

      TreeLog                      VisualizationLog

                         Viz

      Treemap          SVG                  Graph             Statistics

      Inkscape      Browser                     Batch           VizTool

   Annotated Image                              PDF

                            Helmut Simonis         Visualization Techniques   142
                                 Introduction
                 Visualization by Annotation       TreeLog Format
                      Visualization Interface      VisualizerLog Format
                                Conclusions


Architecture (Planned)
           Program + Annotation

                   ECLiPSe

      TreeLog                      VisualizationLog

                         Viz

      Treemap          SVG                  Graph             Statistics

      Inkscape      Browser                     Batch           VizTool

   Annotated Image                              PDF

                            Helmut Simonis         Visualization Techniques   143
                                Introduction
                Visualization by Annotation       TreeLog Format
                     Visualization Interface      VisualizerLog Format
                               Conclusions


CP-Inside
            Program + Annotation

                  CP-Inside

     TreeLog                      VisualizationLog

                        Viz

     Treemap          SVG                  Graph             Statistics

     Inkscape      Browser                     Batch           VizTool

  Annotated Image                              PDF

                           Helmut Simonis         Visualization Techniques   144
                                Introduction
                Visualization by Annotation       TreeLog Format
                     Visualization Interface      VisualizerLog Format
                               Conclusions


Generic Tool
          Program + Annotation

           Your Favourite Tool

      TreeLog                     VisualizationLog

                        Viz                      Your Favourite Analysis

     Treemap          SVG                  Graph             Statistics

     Inkscape      Browser                     Batch           VizTool

  Annotated Image                              PDF

                           Helmut Simonis         Visualization Techniques   145
                               Introduction
               Visualization by Annotation    TreeLog Format
                    Visualization Interface   VisualizerLog Format
                              Conclusions


TreeLog Format



     XML based description
     Record information about nodes in search tree
         Choices
         Failures
         Success
     Redundant information to ease generation




                          Helmut Simonis      Visualization Techniques   146
                                 Introduction
                 Visualization by Annotation    TreeLog Format
                      Visualization Interface   VisualizerLog Format
                                Conclusions


TreeLog Example

  <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
  <tree version="1.0" >
  <root id="0"/>
  <try id="1" parent="0" name="S" size="1" value="9" />
  <fail id="2" parent="1" name="E" size="4" value="4" />
  <try id="3" parent="1" name="E" size="4" value="5" />
  <try id="4" parent="3" name="N" size="1" value="6" />
  <try id="5" parent="4" name="D" size="1" value="7" />
  <try id="6" parent="5" name="M" size="1" value="1" />
  <try id="7" parent="6" name="O" size="1" value="0" />
  <try id="8" parent="7" name="R" size="1" value="8" />
  <try id="9" parent="8" name="Y" size="1" value="2" />
  <succ id="9"/>
  <fail id="10" parent="1" name="E" size="4" value="6" />
  <fail id="11" parent="1" name="E" size="4" value="7" />
  </tree>



                            Helmut Simonis      Visualization Techniques   147
                                 Introduction
                 Visualization by Annotation    TreeLog Format
                      Visualization Interface   VisualizerLog Format
                                Conclusions


TreeLog Example

  <?xml version="1.0" encoding="UTF-8" standalone="yes"?>                          S
                                                                                       9
  <tree version="1.0" >
  <root id="0"/>                                                                   E
                                                                           4       5       6   7
  <try id="1" parent="0" name="S" size="1" value="9" />
                                                                           N
  <fail id="2" parent="1" name="E" size="4" value="4" />                       6
  <try id="3" parent="1" name="E" size="4" value="5" />                    D
  <try id="4" parent="3" name="N" size="1" value="6" />                        7
  <try id="5" parent="4" name="D" size="1" value="7" />                    M
  <try id="6" parent="5" name="M" size="1" value="1" />                        1

  <try id="7" parent="6" name="O" size="1" value="0" />                    O
                                                                               0
  <try id="8" parent="7" name="R" size="1" value="8" />
  <try id="9" parent="8" name="Y" size="1" value="2" />                    R
                                                                               8
  <succ id="9"/>
                                                                           Y
  <fail id="10" parent="1" name="E" size="4" value="6" />                      2
  <fail id="11" parent="1" name="E" size="4" value="7" />
  </tree>



                            Helmut Simonis      Visualization Techniques                           148
                               Introduction
               Visualization by Annotation    TreeLog Format
                    Visualization Interface   VisualizerLog Format
                              Conclusions


VisualizerLog Format



     XML based description
     Describe state of variables and/or constraints at specific
     stages
         Where annotated in program
         For every node in tree
     Linked to search tree log




                          Helmut Simonis      Visualization Techniques   149
                                 Introduction
                 Visualization by Annotation    TreeLog Format
                      Visualization Interface   VisualizerLog Format
                                Conclusions


VisualizerLog Example

  <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
  <visualization version="1.0" >
  <visualizer id="1" type="vector" display="expanded" x="0" y="0"
    width="8" height="10" group="1" min="0" max="9" />
  <state id="1" tree_node="-1" >
  <visualizer_state id="1" >
  <dvar index="1" domain="0 .. 9" />
  <dvar index="2" domain="0 .. 9" />
  <dvar index="3" domain="0 .. 9" />
  <dvar index="4" domain="0 .. 9" />
  <dvar index="5" domain="0 .. 9" />
  <dvar index="6" domain="0 .. 9" />
  <dvar index="7" domain="0 .. 9" />
  <dvar index="8" domain="0 .. 9" />
  </visualizer_state>
  </state>
  ...



                            Helmut Simonis      Visualization Techniques   150
                                 Introduction
                 Visualization by Annotation     TreeLog Format
                      Visualization Interface    VisualizerLog Format
                                Conclusions


VisualizerLog Example


  ...
  <state id="2" tree_node="-1"            >
  <visualizer_state id="1" >
  <dvar index="1" domain="1 ..            9"    />
  <dvar index="2" domain="0 ..            9"    />
  <dvar index="3" domain="0 ..            9"    />
  <dvar index="4" domain="0 ..            9"    />
  <dvar index="5" domain="0 ..            9"    />
  <dvar index="6" domain="0 ..            9"    />
  <dvar index="7" domain="0 ..            9"    />
  <dvar index="8" domain="0 ..            9"    />
  </visualizer_state>
  </state>
  ...




                            Helmut Simonis       Visualization Techniques   151
                                 Introduction
                 Visualization by Annotation     TreeLog Format
                      Visualization Interface    VisualizerLog Format
                                Conclusions


VisualizerLog Example


  ...
  <state id="5" tree_node="1" >
  <visualizer_state id="1" >
  <integer index="1" value="9" />
  <dvar index="2" domain="4 .. 7"               />
  <dvar index="3" domain="5 .. 8"               />
  <dvar index="4" domain="2 .. 8"               />
  <integer index="5" value="1" />
  <integer index="6" value="0" />
  <dvar index="7" domain="2 .. 8"               />
  <dvar index="8" domain="2 .. 8"               />
  <focus group="-" index="1" />
  </visualizer_state>
  </state>
  ...




                            Helmut Simonis       Visualization Techniques   152
                                 Introduction
                 Visualization by Annotation    TreeLog Format
                      Visualization Interface   VisualizerLog Format
                                Conclusions


VisualizerLog Example


  ...
  <state id="6" tree_node="2" >
  <visualizer_state id="1" >
  <integer index="1" value="9" />
  <dvar index="2" domain="4 .. 7" />
  <dvar index="3" domain="5 .. 8" />
  <dvar index="4" domain="2 .. 8" />
  <integer index="5" value="1" />
  <integer index="6" value="0" />
  <dvar index="7" domain="2 .. 8" />
  <dvar index="8" domain="2 .. 8" />
  <failed group="-" index="2" value="4" />
  </visualizer_state>
  </state>
  ...




                            Helmut Simonis      Visualization Techniques   153
                                 Introduction
                 Visualization by Annotation    TreeLog Format
                      Visualization Interface   VisualizerLog Format
                                Conclusions


VisualizerLog Example


  ...
  <state id="14" tree_node="9"            >
  <visualizer_state id="1" >
  <integer index="1" value="9"            />
  <integer index="2" value="5"            />
  <integer index="3" value="6"            />
  <integer index="4" value="7"            />
  <integer index="5" value="1"            />
  <integer index="6" value="0"            />
  <integer index="7" value="8"            />
  <integer index="8" value="2"            />
  </visualizer_state>
  </state>
  ...
  </visualization>




                            Helmut Simonis      Visualization Techniques   154
                                     Introduction
                     Visualization by Annotation
                          Visualization Interface
                                    Conclusions


Outline


  1   Introduction

  2   Visualization by Annotation

  3   Visualization Interface

  4   Conclusions




                                Helmut Simonis      Visualization Techniques   155
                               Introduction
               Visualization by Annotation
                    Visualization Interface
                              Conclusions


Conclusions



     New ELearning course for ECLiPSe
     Open source material, Creative Commons BY-NC-SA
     license
         Application driven
         Modelling with global constraints
         Customizing search
     Effort only justifiable through Cisco grant




                          Helmut Simonis      Visualization Techniques   156
                                 Introduction
                 Visualization by Annotation
                      Visualization Interface
                                Conclusions


Visualization



      Design choice: System independent
      Provide enough information to user of system, not to tool
      developer
      Relatively few primitives, extensible for specific global
      constraints
      XML intermediate format, open for specific analysis




                            Helmut Simonis      Visualization Techniques   157

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:4
posted:12/14/2011
language:Latin
pages:157