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2010-02-26       4   Erlang
1/2
??   No Erlang
??


??
     ??           3

??
     ??   Chord
     ??   VectorClocks
     ??
2/2
??
     ??


??
     ??                   

                          
               
          
       Chord
          EpiChord
              
   BASE            Sinfonia:
                   VectorClocks                         
          
       Bloom       
   ZDD
                                         EpiChord
Lookup
??
??
                                          1
                        0-10
    1
              5?
                        11-20
   2
       2
                        21-30
   3
                                          3
??
     ??
     ??
??
     ??             !
     ??   ?
B. Leong et al. http://www.comp.nus.edu.sg/~bleong/slides/icon-epichord-slides.pdf
     


Address Space

                                           0-63
B. Leong et al. http://www.comp.nus.edu.sg/~bleong/slides/icon-epichord-slides.pdf
     


Mapping Keys to Nodes

                                                 




         1-6
          6
           :
     :
         52-57
        57
           :
     :
B. Leong et al. http://www.comp.nus.edu.sg/~bleong/slides/icon-epichord-slides.pdf
    


Chord
                               


            35    
    36-40
       40
    41-47
       47
    48-50
       49
    51-2
        57
    3-30
        6




                       ??     log

                      ??     log
B. Leong et al. http://www.comp.nus.edu.sg/~bleong/slides/icon-epichord-slides.pdf
     


EpiChord Lookup Algorithm
B. Leong et al. http://www.comp.nus.edu.sg/~bleong/slides/icon-epichord-slides.pdf
     


EpiChord Lookup Algorithm
B. Leong et al. http://www.comp.nus.edu.sg/~bleong/slides/icon-epichord-slides.pdf
     


EpiChord Lookup Algorithm
B. Leong et al. http://www.comp.nus.edu.sg/~bleong/slides/icon-epichord-slides.pdf
     


EpiChord Lookup Algorithm
B. Leong et al. http://www.comp.nus.edu.sg/~bleong/slides/icon-epichord-slides.pdf
     


EpiChord Lookup Algorithm
B. Leong et al. http://www.comp.nus.edu.sg/~bleong/slides/icon-epichord-slides.pdf
     


EpiChord Lookup Algorithm
B. Leong et al. http://www.comp.nus.edu.sg/~bleong/slides/icon-epichord-slides.pdf
     


EpiChord Lookup Algorithm
B. Leong et al. http://www.comp.nus.edu.sg/~bleong/slides/icon-epichord-slides.pdf
     


EpiChord Lookup Algorithm
B. Leong et al. http://www.comp.nus.edu.sg/~bleong/slides/icon-epichord-slides.pdf
     EpiChord


Division of Address Space


                   ?
J. Xu et al., On the Fundamental Tradeoffs between Routing Table Size and Network Diameter in Peer-to-Peer Networks
    


                                                                                           Lookup

                         
                                                                                                                         
                                                                                (Dynamo?)


                                                EpiChord?
??
??
     ??   ACID:
                           1.? SELECT 
                           2.? INSERT 
                           3.?    :
          DB

??
     ??   1                               ?
??
     ??                !
     ??           ?
S. Shinohara http://www.slideshare.net/shino/conflict-resolution-in-kai-presentation
       VectorClocks


 happens-before (->)




BASE                              VectorClocks
S. Shinohara http://www.slideshare.net/shino/conflict-resolution-in-kai-presentation
       VectorClocks


 concurrent (||)




BASE                              VectorClocks
T.Yamamuro
     


(postgresqls) 2-phase commit
T.Yamamuro
     Sinfonia


2-phase commits optimization




 
                                      ?
T.Yamamuro
      Sinfonia


mini-transaction primitives
T.Yamamuro
     Sinfonia


Sinfonias 2-phase commit
                 =
T.Yamamuro
     Sinfonia


Sinfonia 2-phase commit 5
T.Yamamuro
     Sinfonia


Sinfonia 2-phase commit 5
T.Yamamuro
     Sinfonia


Sinfonia 2-phase commit 5
T.Yamamuro
              Sinfonia


 Evaluation: Scalability

                                    NFS,   




250                             
          2               100
VectorClocks




                Sinfonia
                        2-phase commit

                                              
        BASE
         ACID
??
??


            {apple, banana} + {orange}            Is apple a member?
          = {apple, banana, orange}
             {apple, banana, orange}
                             
                                
??
     ??
     ??
??
     ??                  !
     ??   ?                      Q.          ?
                                 A. BigTable
                                        Bloom
Bloom filter
??
               
       
      BF
                      m          
             0
 0
 0
 0
 0
 0
 0
 0
      ZF
                          m           
      hi
          i               0<i   k 
                                         [0,m-1]                  hi(x)
??
                                                        0
 1
 0
 0
 1
 0
 0
 0
     ??   BF = ZF
??
     ??   BF[ hi(x) ] = 1                                         hi(y)

                                                        0
 1
 0
 0
 1
 1
 0
 0

                           
                       Bloom filter m=8, k=2   x, y
Bloom filter
??             membership query
     ??   F = ZF
                                          hi(x)
   included
     ??   F[ hi(x) ] = 1
     ??   BF & F == F             0
 1
 0
 0
 1
 1
 0
 0


                                          hi(z)
   not included

                                  0
 1
 0
 0
 1
 1
 0
 0

                                                      false positive!
                                          hi(w)
 included

                                  0
 1
 0
 0
 1
 1
 0
 0
Bloom filter
??
     ??   O k
     ??             n
     ??
Bloom filter
??             OR AND
     ??       m,            hi           

                                 0
 1
 0
 0
 1
 1
 0
 0



                                 0
 0
 0
 1
 1
 0
 0
 1


                                 0
 1
 0
 1
 1
 1
 0
 1
Bloom filter                              false positive
    ??                                    p
                     ? 1 ? kn   ? kn ?
                 p = ?1? ?  exp? ? ?
                     ? m?       ? m?

    ??                            f   

                             k
                 f = (1? p)




                                                        m = 256, n = 32
Bloom filter                            false positive
    ??   f                     k                        
         ??   f        k
                  ?     m?
              k = ?ln2 ? ?
                  ?     n?
         ??   floor
               ?? k
                  ??


    ??                         f
       
                               m
                  f  0.6185   n

                           k
Bloom filter
    ??   n, f                             m   

                 m = ?1.44n log 2 f
                          k
Bloom filter
    ??                                        b       

                  b = ?1.44 log 2 f
                                      k           
         ??                           
                  b = ?log 2 f                                  9.6       1%
        ??   1.44                                                    
                  ??


                                                         9.6   

    ??                 Bloom filter
         ??                               b
                                                                          1%
Bloom filter
    ??                k                                     p
                     1
                  p=                                 0
 1
 0
 0
 1
 1
 0
 1
                     2
                      k       
                            Bloom filter   

         ??                       [mitzenmacher02]

    ??                k
         ??   0   1
         ??
S. Minato http://www-alg.ist.hokudai.ac.jp/~minato/alg2009-j.html
      ZDD
BDD (Binary Decision Diagram)


                          {abc, ab, ac, b, } 
           trie                  



 0 (false)
   1 (true)
S. Minato http://www-alg.ist.hokudai.ac.jp/~minato/alg2009-j.html
     ZDD


BDD
S. Minato http://www-alg.ist.hokudai.ac.jp/~minato/alg2009-j.html
     ZDD


BDD
S. Minato http://www-alg.ist.hokudai.ac.jp/~minato/alg2009-j.html
    ZDD
S. Minato http://www-alg.ist.hokudai.ac.jp/~minato/alg2009-j.html
    ZDD
S. Minato http://www-alg.ist.hokudai.ac.jp/~minato/alg2009-j.html
    ZDD
           BDD
ZDD: Zero-suppressed BDD
S. Minato http://www-alg.ist.hokudai.ac.jp/~minato/alg2009-j.html
     ZDD


ZDD
S. Minato http://www-alg.ist.hokudai.ac.jp/~minato/alg2009-j.html
     ZDD


ZDD
S. Minato http://www-alg.ist.hokudai.ac.jp/~minato/alg2009-j.html
     ZDD


ZDD
??
     ??


??
     ??   EpiChord
          ??   B. Leong et al., EpiChord: Parallelizing the Chord lookup algorithm with reactive
               routing state management, Comput. Commun., vol.29, no.9, pp.1243-1259, 2006.
??
     ??   Sinfonia
          ??   M.K. Aguilera et al., Sinfonia: a new paradigm for building scalable distributed systems,
               Proc. of SOSP07, pp.159-174, 2007.
??
     ??   ZDD
          ??   S. Minato, Zero-suppressed BDDs for set manipulation in combinatorial problems,
               Proc. of DAC93, pp. 272-277, 1993.

??
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