A Self-Stabilizing Algorithm for Maximal Matching in Link-Register Model

Abstract

This paper presents a new distributed self-stabilizing algorithm solving the maximal matching problem under the fair distributed daemon. This is the first maximal matching algorithm in the link-register model under read/write atomicity. This work is composed of two parts. As we cannot establish a move complexity analysis under the fair distributed daemon, we first design an algorithm $\mathcal A_{1}$ under the unfair distributed daemon dealing with some relaxed constraints on the communication model. Second, we adapt $\mathcal A_{1}$ so that it can handle the fair distributed daemon, leading to the $\mathcal A_{2}$ algorithm. We prove that algorithm $\mathcal A_1$ stabilizes in $O(m\Delta )$ moves and algorithm $\mathcal A_2$ in $O(m\Delta )$ rounds, with $\Delta$ the maximum degree and m the number of edges.