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Brief Announcement: Efficient Self-Stabilizing 1-Maximal Matching Algorithm for Arbitrary Networks

Abstract : We present a new self-stabilizing 1-maximal matching algorithm that works under the distributed unfair daemon for arbitrarily shaped networks. The 1-maximal matching is a 2/3-approximation of a maximum matching, a significant improvement over the 1/2-approximation that is guaranteed by a maximal matching. Our algorithm is efficient (its stabilization time is $O(e)$ moves, where $e$ denotes the number of edges in the network). Besides, our algorithm is optimal with respect to identifiers locality (we assume node identifiers are distinct up to distance three, a necessary condition to withstand arbitrary networks). The proposed algorithm closes the complexity gap between two recent works: Inoue et al. presented a 1-maximal matching algorithm that is $O(e)$ moves but requires the network topology not to contain a cycle of size of multiple of three ; Cohen et al. consider arbitrary topology networks but requires $O(n^3)$ moves to stabilize (where $n$ denotes the number of nodes in the network). Our solution preserves the better complexity of $O(e)$ moves, yet considers arbitrary networks, demonstrating that previous restrictions were unnecessary to preserve complexity results.
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https://hal.sorbonne-universite.fr/hal-01520336
Contributor : Sébastien Tixeuil Connect in order to contact the contributor
Submitted on : Wednesday, May 10, 2017 - 1:15:43 PM
Last modification on : Friday, January 8, 2021 - 5:38:04 PM

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  • HAL Id : hal-01520336, version 1

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Michiko Inoue, Fukuhito Ooshita, Sébastien Tixeuil. Brief Announcement: Efficient Self-Stabilizing 1-Maximal Matching Algorithm for Arbitrary Networks. ACM Conference on Principles of Distributed Computing (PODC 2017) , Jul 2017, Washington, United States. ⟨hal-01520336⟩

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