A New Self-Stabilizing Maximal Matching Algorithm

TL;DR

This paper introduces a unified self-stabilizing algorithm for maximal matching that matches or improves upon previous algorithms in terms of stabilization time and move complexity across various distributed daemon models.

Contribution

A single self-stabilizing algorithm that unifies previous approaches and improves move complexity for the distributed adversarial daemon.

Findings

Stabilizes in same moves as previous best algorithms for multiple daemon models.

Reduces move complexity for distributed adversarial daemon from O(n^2) and O(δm) to O(m).

Works efficiently across different distributed daemon settings.

Abstract

The maximal matching problem has received considerable attention in the self-stabilizing community. Previous work has given different self-stabilizing algorithms that solves the problem for both the adversarial and fair distributed daemon, the sequential adversarial daemon, as well as the synchronous daemon. In the following we present a single self-stabilizing algorithm for this problem that unites all of these algorithms in that it stabilizes in the same number of moves as the previous best algorithms for the sequential adversarial, the distributed fair, and the synchronous daemon. In addition, the algorithm improves the previous best moves complexities for the distributed adversarial daemon from O(n^2) and O(delta m) to O(m) where n is the number of processes, m is thenumber of edges, and delta is the maximum degree in the graph.