Self-Stabilizing Maximal Matching and Anonymous Networks

TL;DR

This paper introduces a self-stabilizing algorithm for maximal matching in anonymous networks, achieving $O(n^3)$ moves, and addresses the challenge of node anonymity by assigning unique link names.

Contribution

It presents the first self-stabilizing maximal matching algorithm for anonymous networks and solves the anonymity issue with a link-naming technique.

Findings

Algorithm stabilizes in $O(n^3)$ moves with high probability

Provides a method for unique link naming in anonymous networks

Addresses the contradiction in anonymous assumptions

Abstract

We propose a self-stabilizing algorithm for computing a maximal matching in an anonymous network. The complexity is $O(n^3)$ 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.