2011 IEEE International Symposium on Parallel and Distributed Processing Workshops and Phd Forum (2011)
Anchorage, Alaska USA
May 16, 2011 to May 20, 2011
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.
P. Robinson, U. Schmid and M. Biely, "Solving k-Set Agreement with Stable Skeleton Graphs," 2011 IEEE International Symposium on Parallel and Distributed Processing Workshops and Phd Forum(IPDPSW), Anchorage, Alaska USA, 2011, pp. 1488-1495.