A self-stabilizing 2/3-approximation algorithm for the maximum matching problem

Abstract : The matching problem asks for a large set of disjoint edges in a graph. It is a problem that has received considerable attention in both the sequential and self-stabilizing literature. Previous work has resulted in self-stabilizing algorithms for computing a maximal ($\frac{1}{2}$-approximation) matching in a general graph, as well as computing a $\frac{2}{3}$-approximation on more specific graph types. In the following we present the first self-stabilizing algorithm for finding a $\frac{2}{3}$-approximation to the maximum matching problem in a general graph. We show that our new algorithm stabilizes in at most exponential time under a distributed adversarial daemon, and $O(n^2)$ rounds under a distributed fair daemon, where $n$ is the number of nodes in the graph.
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https://hal.archives-ouvertes.fr/hal-01303005
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Submitted on : Friday, April 15, 2016 - 4:18:06 PM
Last modification on : Thursday, March 21, 2019 - 1:06:11 PM

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Fredrik Manne, Morten Mjelde, Laurence Pilard, Sébastien Tixeuil. A self-stabilizing 2/3-approximation algorithm for the maximum matching problem. International Conference on Stabilization, Safety, and Security (SSS 2008), Nov 2008, Detroit, MI, United States. pp.94-108, ⟨10.1007/978-3-540-89335-6_10⟩. ⟨hal-01303005⟩

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