A self-stabilizing algorithm for maximal matching in link-register model in $O(nΔ^3)$ moves

In the matching problem, each node maintains a pointer to one of its neighbor or to null, and a maximal matching is computed when each node points either to a neighbor that itself points to it (they are then called married), or to null, in which case no neighbor can also point to null. This paper presents a self-stabilizing distributed algorithm to compute a maximal matching in the link-register model under read/write atomicity, with complexity O(n∆) moves under the adversarial distributed daemon, where ∆ is the maximum degree of the graph.