Self-Stabilizing Maximal Matching and Anonymous Networks

We propose a self-stabilizing algorithm for computing a maximal matching in an anonymous network. The complexity is O(n) moves with high probability, under the adversarial distributed daemon. In this algorithm, each node can determine whether one of its neighbors points to it or to another node, leading to a contradiction with the anonymous assumption. To solve this problem, we provide under the classical link-register model, a self-stabilizing algorithm that gives a unique name to a link such that this name is shared by both extremities of the link.