Abstract
We propose a new self-stabilizing 1-maximal matching algorithm that works under the distributed unfair daemon for arbitrarily shaped networks without cycle whose length is a multiple of three. The 1-maximal matching is a \(\frac{2}{3}\)-approximation of a maximum matching, a significant improvement over the \(\frac{1}{2}\)-approximation that is guaranteed by a maximal matching.
Our algorithm is as efficient (its stabilization time is O(e) moves, where e denotes the number of edges in the network) as the best known algorithm operating under the weaker central daemon. It significantly outperforms the only known algorithm for the distributed daemon (with O(e) moves vs. \(O(2^n \delta n)\) moves, where \(\delta \) denotes the maximum degree of the network, and n its number of nodes), while retaining its silence property (after stabilization, its output remains fixed).
This work was supported by JSPS KAKENHI Grant Numbers 26330084 and 15H00816. Part of this work was carried out while the third author was visiting NAIST thanks to Erasmus Mundus TEAM program.
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Notes
- 1.
We say matching M is an \(\alpha \)-approximation of the maximum matching if \(|M| \ge \alpha |M_{max}|\) holds, where \(M_{max}\) is a maximum matching.
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Inoue, M., Ooshita, F., Tixeuil, S. (2016). An Efficient Silent Self-stabilizing 1-Maximal Matching Algorithm Under Distributed Daemon Without Global Identifiers. In: Bonakdarpour, B., Petit, F. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2016. Lecture Notes in Computer Science(), vol 10083. Springer, Cham. https://doi.org/10.1007/978-3-319-49259-9_17
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