A Failure Detector for k-Set Agreement in Asynchronous Dynamic Systems

Élise Jeanneau (1) , Thibault Rieutord (2, 1) , Luciana Arantes (3, 1, 4) , Pierre Sens (5, 1, 3, 4)

1 LIP6 - Laboratoire d'Informatique de Paris 6
2 ENS Cachan Bretagne - École normale supérieure - Cachan, antenne de Bretagne
3 UPMC - Université Pierre et Marie Curie - Paris 6
4 Regal - Large-Scale Distributed Systems and Applications
5 Inria Paris-Rocquencourt

The k-set agreement problem is a generalization of the consensus problem where processes can decide up to k different values. Very few papers have tackled this problem in dynamic networks, and to the best of our knowledge, every algorithm proposed so far for k-set agreement in dynamic networks assumed synchronous communications. Exploiting the formalism of the Time-Varying Graph model, this paper proposes a new failure detector Sigma-bottom-k, based on Sigma-k and Sigma-bottom, for solving k-set agreement in asynchronous dynamic networks. We present two algorithms that implement this new failure detector, making assumptions on the number of process failures and graph connectivity. We also provide an algorithm for solving k-set agreement using Sigma-bottom-z , under an assumption on the relative values of k and z.

Mots clés: k-set agreement; failure detectors; dynamic networks; time-varying graphs; asyn-chronous systems; evolving membership

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

Élise Jeanneau, Thibault Rieutord, Luciana Arantes, Pierre Sens. A Failure Detector for k-Set Agreement in Asynchronous Dynamic Systems. [Research Report] RR-8727, UPMC Sorbonne Universités/CNRS/Inria - EPI REGAL. 2015. ⟨hal-01151739v1⟩