Data Distribution in a Peer to Peer Storage System by suchenfz

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									   Data Distribution in a
Peer to Peer Storage System

 Cyril Randriamaro, Olivier Soyez,
   Gil Utard, Francis Wlazinski
Objectives

Sharing data space

Data perennity

Data ubiquitous



                     2
       Solution : P2P




File
          Blocks


                   Fragments
                       (f)
                               Peers (N)
                                           3
Block Storage




                4
Block Reconstruction




                       5
Block Reconstruction




                       6
Storage Example
Peers Number N: 1000
Blocks Number NB: 100000
Fragment Size: 1 Mb
Fragments Number f: 11
Each Peer stores (100000x11)/1000=1100 Fragments
One Peer fails :
 1100 x 10 Fragments  11 Gb
   999 Peers                   11 Mb

                Data Distribution
                                                   7
Distribution
Mapping Blocks to Peers


                     1 fragment per peer




                  Notation
                                           8
Distribution
Mapping Blocks to Peers




                          9
Distribution
Reconstruction Cost




             2
                      10
Distribution
Intersection Size  1



                1


                    1
                        11
Problem Formulation
Minimize the reconstruction cost for all peers
  Managed by distribution
  Reconstruction cost=1


Find an optimal distribution of cost=1, i.e
  Intersection between two different blocks  1
  Store a maximum number of blocks




                                                  12
Around One Peer
             N: the peer number
             NBmax: the maximum number
             of stored blocks
             f: fragments number / block
             : fragments number / peer
             Bi: block i, set of f peers

                             Bi            Bj

                   = (N-1) / (f-1)
                  NBmax=N *  / f


                                                13
Finite Affine Plane
Optimal distribution
  Nbmax=(f²*((f²-1)/(f-1)))/f=(f+1)*f


Restrictions
  The fragments number f is prime
  The peers number is N = f2

Open problem
  For many values of f
  Since 1782
                                        14
Finite Affine Plane
Lines


             1      2     3


             4      5     6

             7      8     9


        3 fragments/Block, 9 peers
                                     15
Finite Affine Plane
Columns


          1   2   3


          4   5   6

          7   8   9




                      16
Finite Affine Plane
Diagonals of distance 0


              1     2     3


              4     5     6

              7     8     9




                              17
Finite Affine Plane
Diagonals of       distance 1


               1       2        3


               4       5        6

               7       8        9




                                    18
Finite Affine Plane
Diagonals of distance 0


              1      2    3


              4      5    6

              7      8    9




                              19
Finite Affine Plane
Diagonals of distance 1


              1      2    3


              4      5    6

              7      8    9




                              20
Other Optimal Distribution
Finite projective plane of order (f-1)
  Point = peer
  Line = block
Optimal distribution
  Nbmax=((f²-f+1)*((f²-f)/(f-1)))/f=f²-f+1
Restrictions
  The fragments number f is prime
  The peers number is N = f²-f+1



                                             21
Our new Distribution
Matrices construction
  Prime numbers theory
Features:
  f is a prime number
  For all N, with N f²  asymptotically optimal
Optimal
  For many values of N




                                                   22
Our new Distribution
3 fragments/Block and 9 peers
                                1   4   7
                                1   5   9
                                1   2   3
        1    2    3             2   5    8
                                2   6    8
        4    5    6             3   5    7
                                3   6    9
        7    8    9             4   5   6
                                7   8   9



                                             23
Comparison




             24
      Analysis
     Our distribution              Our distribution
     versus Optimal                versus Random
Our distribution
                       –           Our distribution
                                                         –
Optimal distribution
                       –           Random distribution
                                                         –



                       11 fragments/Block
                                                             25
   Analysis
   Our distribution                Our distribution
   versus Optimal                  versus Random
Our distribution
                       –           Our distribution
                                                         –
Optimal distribution
                       –           Random distribution
                                                         –



                       7 fragments/Block
                                                             26
Conclusion
Our Distribution
 Experimental results
 Asymptotically optimal
 For all N, f prime number
Open problems
 Optimal construction?
 Mathematical proof
Future works
 Dynamic way


                             27
Thank you!



 THANK YOU FOR YOUR ATTENTION!




                                 28
                                          1       2       3

Metapeers                             4       5       6

                                  7       8       9




          1
                      2       3
      4
                          6
                  5

  7
              8       9


                                                              29

								
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