Abstract

We define the k-set consensus problem as an extension of the consensus problem, where each processor decides on a single value such that the set of decided values in any run is of size at most k. We require the agreement condition that all values decided upon are initial values of some processor. We show that the problem has a simple (k - 1)-resilient protocol in a totally asynchronous system. In an attempt to come up with a matching lower bound on the number of failures, we study the uncertainty condition, which requires that there must be some initial configuration from which all possible input values can be decided. We prove using a combinatorial argument that any k-resilient protocol for the k-set agreement problem would satisfy the uncertainty condition, while this is not true for any (k - 1)-resilient protocol.

Citations

1300	Impossibility of distributed consensus with one faulty process - Fischer, Lynch, et al. - 1985
178	Another advantage of free choice: completely asynchronous agreement protocols - Ben-Or - 1983
152	Randomized Byzantine generals - Rabin - 1983
150	Abu-Amara H., Memory requirements for agreement among unreliable asynchronous processes - Loui - 1987
35	Achievable cases in an asynchronous environment - Attiya, Bar-Noy, et al. - 1987
32	A combinatorial characterization of the distributed tasks which are solvable in the presence of one faulty processor - Biran, Moran, et al. - 1988
18	Fault-tolerant decision making in totally asynchronous distributed systems - Bridgland, Watro - 1987
13	Asynchronous Byzantine consensus - ATTIYA, DOLEV, et al.
10	Impossibility results in the presence of multiple faulty processes - Taubenfeld, Katz, et al. - 1994
1	A revised version appeared - IEEE - 1983
1	Some CombinatoriM Lemmas in Topology - Kuhn - 1960