An Efficient Silent Self-stabilizing 1-Maximal Matching Algorithm Under Distributed Daemon 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 $\frac{2}{3}$-approximation of a maximum matching, a significant improvement over the $\frac{1}{2}$-approximation that is guaranteed by a maximal matching. Our algorithm is 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.

A preliminary brief announcement of this work appears in the proceedings of the 36th ACM Symposium on Principles of Distributed Computing (PODC 2017). This work was supported by JSPS KAKENHI Grant Number 26330084. Part of this work was carried out while the third author was visiting NAIST thanks to Erasmus Mundus TEAM program.