Upper bounds for stabilization in acyclic preference-based systems

Authors:
Fabien Mathieu
Affiliations:
Orange Labs, Issy-les-Moulineaux, France
Venue:
SSS'07 Proceedings of the 9h international conference on Stabilization, safety, and security of distributed systems
Year:
2007

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Abstract

Preference-based systems (p.b.s.) describe interactions between nodes of a system that can rank their neighbors. Previous work has shown that p.b.s. converge to a unique locally stable matching if an acyclicity property is verified. In the following we analyze acyclic p.b.s. with respect to the self-stabilization theory. We prove that the round complexity is bounded by n/2 for the adversarial daemon. The step complexity is equivalent to n2/4 for the round robin daemon, and exponential for the general adversarial daemon.