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M. Biely, P. Robinson, U. Schmid:
"Solving k-Set Agreement with Stable Skeleton Graphs";
Vortrag: International Parallel and Distributed Processing Symposium (IPDPS), Anachorage, Alaska; 16.05.2011 - 20.05.2011; in: "IPDPS Workshops", (2011), ISBN: 978-1-61284-425-1; S. 1488 - 1495.

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.

http://dx.doi.org/10.1109/IPDPS.2011.301