An Efficient Silent Self-Stabilizing 1-Maximal Matching Algorithm in Anonymous Networks

We propose a new self-stabilizing 1-maximal matching algorithm which is silent and works for any anonymous networks without a cycle of length of a multiple of 3 under a central unfair daemon. The 1-maximal matching is a 2 3 -approximation to the maximum matching, and expected to get more matching pairs than a maximal matching, which only guarantees a 1 2 -approximation. The time complexity of the proposed algorithm is O(e) moves, which is O(n) moves if we restrict the topology to trees or rings whose length is not a multiple of 3, where n and e be the numbers of nodes and edges in a graph, respectively. The best existing result for 1-maximal matching for anonymous networks is an algorithm of Goddard et al. [8] which works for anonymous trees and anonymous rings whose length is not a multiple of 3 under a central daemon, and the time complexity is O(n) moves. Therefore, the result in this paper is a significant improvement from the best existing results. Submitted: March 2015 Reviewed: August 2015 Revised: August 2015 Accepted: September 2015 Final: January 2016 Published: February 2016 Article type: Regular paper Communicated by: M. S. Rahman and E. Tomita This work was supported by JSPS KAKENHI Grant Numbers 26330084 and 15H00816. E-mail addresses: [email protected] (Yuma Asada) [email protected] (Fukuhito Ooshita) [email protected] (Michiko Inoue) 60 Asada et al. Silent Anonymous Self-Stabilizing 1-Maximal Matching a b c d (a) a b c d (b) Figure 1: A maximal matching and a 1-maximal matching. The matching in (a) is maximal but not 1-maximal. The matching in (b) is 1-maximal.