Introduction to Distributed Algorithm Part One_ Protocols Chapter 2

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					Introduction to Distributed Algorithm
      Part Two: Fundamental Algorithm
              Chapter 7- Election Algorithms




                Teacher: Chun-Yuan Lin




  4/11/2014               Election Algorithms   1
           Election Algorithms (1)
n   In this chapter the problem of election, also called leader finding, will
    be discussed. The election problem was first posed by LeLann
    (Subsection 7.2.1 ).
    n   The problem is to start from a configuration where all processes are in
        the same state, and arrive at a configuration where exactly one process is
        in state leader and all other processes are in the state lost.


n   An election under the processes must be held if a centralized
    algorithm is to be executed and there is no a priori candidate to serve
    as the initiator of this algorithm.

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          Election Algorithms (2)
n   A large number of results about the election problem exist.




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          Introduction (1)
n   The process in state leader at the end of the computation is called the
    leader and is said to be elected by the algorithm.




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Introduction (2)




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    Assumptions Made in this Chapter (1)
n   The election problem has been studied in this chapter under
    assumptions that we now review




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Assumptions Made in this Chapter (2)




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          Elections and Waves
n   Election with the tree algorithm (find smallest identity)



n   Election with the phase algorithm



n   Election with Finn's algorithm




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                                  (leave to root)
                                  (root to leave)




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          Ring Networks (1)
n   In this section some election algorithms for unidirectional rings are
    considered. The election problem was first posed for the context of
    ring networks by LeLann (message complexity O(N2) ).

n   This solution was improved by Chang and Roberts (worst case
    complexity O(N2), average case complexity O(NlogN)).

n   Hirschberg-Sinclair algorithm required channels to be bidirectional
    (worst case complexity O(NlogN)).


          4/11/2014                 Election Algorithms                     10
          Ring Networks (2)
n   Petersen and Dolev, Klawe, and Rodeh independently proposed all
    O(NlogN) solution for the unidirectional ring.

n   A worst case lower bound of 0.34N log N messages for bidirectional
    rings was proved by Bodlaender.

n   Pachl, Korach, and Rotem proved lower bounds of Ω(NlogN) for the
    average case complexity, both for bidirectional and unidirectional
    rings.


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         The Algorithms of LeLann and of
         Chang and Roberts (1)
n   The Algorithms of LeLann



                                                     (more than one initiator)
                                                     (some are not initiator)
                                                      (receive all tok)
                                                        unidirectional rings




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         The Algorithms of LeLann and of
         Chang and Roberts (2)


n   The Algorithms of Chang and Roberts




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4/11/2014   (only pass better tok) Election Algorithms   unidirectional rings   14
The Peterson/Dolev-Klawe-Rodeh
Algorithm




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                                  (until only one active)




                                   (not, send again)




                                   unidirectional rings

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          A Lower-bound Result (1)
n   The result is due to Pachl, Korach, and Rotem and is obtained under
    the following assumptions.




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A Lower-bound Result (2)




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Arbitrary Networks




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Extinction and a Fast Algorithm
              (1)




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Extinction and a
Fast Algorithm
(2)
                   (only one wave)




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The Gallager-Humblet-Spira Algorithm (1)




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The Gallager-Humblet-Spira Algorithm (2)




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Global Description of the GHS Algorithm (1)




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Global Description of the GHS Algorithm (2)




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Global Description of the GHS Algorithm (3)




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Detailed
Description
of the GHS
Algorithm
(1)




      4/11/2014   Election Algorithms   27
Detailed
Description
of the GHS
Algorithm
(2)




      4/11/2014   Election Algorithms   28
Detailed
Description of
the GHS
Algorithm (3)




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The Korach-Kutten-Nloran Algorithm




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4/11/2014   Election Algorithms   31
Applications of the KKM Algorithm




   4/11/2014   Election Algorithms   32

				
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