k-set agreement with limited accuracy failure detectors

• Authors: Achour Mostéfaoui;Michel Raynal
• Venue: Proceedings of the nineteenth annual ACM symposium on Principles of distributed computing
• Year: 2000

Let the scope of the accuracy property of an unreliable failure detector be the number x of processes that may not suspect a correct process. The scope notion gives rise to new classes of failure detectors among which we consider Sx and ⋄Sx in this paper (Usual failure detectors consider an implicit scope equal to n, the total number of processes).The k-set agreement problem generalizes the consensus problem: each correct process has to decide a value in such a way that a decided value is a proposed value, and the number of decided values is bounded by k. There exist protocols that solve this problem in asynchronous distributed systems when ƒ k (where ƒ is the maximum number of processes that may crash). Moreover, it has been shown that there is no solution in those systems when ƒ ≥ k. The paper considers asynchronous distributed systems equipped with limited scope accuracy failure detectors. It studies conditions on n, ƒ, k and x that allow to solve the k-set agreement problem in those systems and presents two protocols. The first protocol solves the k-set agreement in asynchronous distributed systems augmented with a failure detector of the class Sx. It requires ƒ k + x - 1. The second protocol works with any failure detector of the class ⋄Sx. It actually defines a family of protocols. This family allows to solve the k-set agreement problem when ƒ max(k, max1≤&agr;≤k(min(n - &agr;⌊n/(&agr; + 1)⌋, &agr; +x - 1))). We conjecture that, when ƒ ≥ k, these conditions are necessary to solve the k-set agreement problem in asynchronous distributed systems equipped with failure detectors &egr; Sx or ⋄Sx, respectively.