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(nΔ3)} moves under the adversarial distributed daemon, where Δ is the maximum degree of the graph.
@article{arxiv.1709.04811,
title = {A self-stabilizing algorithm for maximal matching in link-register model in $O(n\Delta^3)$ moves},
author = {Johanne Cohen and Georges Manoussakis and Laurence Pilard and Devan Sohier},
journal= {arXiv preprint arXiv:1709.04811},
year = {2017}
}