In this paper we consider the k-set agreement problem in distributed
message-passing systems using a round-based approach: Both synchrony of
communication and failures are captured just by means of the messages that
arrive within a round, resulting in round-by-round communication graphs that
can be characterized by simple communication predicates. We introduce the weak
communication predicate PSources(k) and show that it is tight for k-set
agreement, in the following sense: We (i) prove that there is no algorithm for
solving (k-1)-set agreement in systems characterized by PSources(k), and (ii)
present a novel distributed algorithm that achieves k-set agreement in runs
where PSources(k) holds. Our algorithm uses local approximations of the stable
skeleton graph, which reflects the underlying perpetual synchrony of a run. We
prove that this approximation is correct in all runs, regardless of the
communication predicate, and show that graph-theoretic properties of the stable
skeleton graph can be used to solve k-set agreement if PSources(k) holds.Comment: to appear in 16th IEEE Workshop on Dependable Parallel, Distributed
and Network-Centric System