On the Uniformity of Peer Sampling based on View Shuffling

Yann Busnel (1) , Roberto Beraldi (2) , Roberto Baldoni (2)

1 LINA - Laboratoire d'Informatique de Nantes Atlantique
2 MIDLAB - Middleware Laboratory

Consider a group of peers, an ideal random peer sampling service should return a peer, which is a uniform independent random sample of the group. This paper focuses on the implementation and analysis of a peer sampling service based on symmetric view shuffling, where each peer is equipped with a local view of size c, representing a uniform random sample of size c of the whole system. To this end, pairs of peers regularly and continuously swap a part of their local views (shuffle operation). The paper provides the following formal proofs: (i) starting from any non-uniform distribution of peers in the peers' local views, after a sequence of pairwise shuffle operations, each local view eventually represents a uniform sample of size c; (ii) once previous property holds, any successive sequence of shuffle operations does not modify this uniformity property and (iii) a lower bound for convergence speed. This paper also presents some numerical results concerning the speed of convergence to uniform samples of the local views.

Mots clés: Numerical evaluation; Stochastic process; Theoretical analysis; Peer sampling; Gossip-based protocol; Numerical evaluation

Domaines: Calcul parallèle, distribué et partagé [cs.DC]

Yann Busnel, Roberto Beraldi, Roberto Baldoni. On the Uniformity of Peer Sampling based on View Shuffling. Journal of Parallel and Distributed Computing, 2011, 71 (8), pp.1165-1176. ⟨10.1016/j.jpdc.2011.01.009⟩. ⟨hal-03687435⟩