Short paper: Tight bounds for universal and cautious self-stabilizing 1-maximal matching

Abstract

We consider the problem of constructing a matching in an n-nodes graph in a distributed and self-stabilizing manner. We prove that there exists a lower bound in space of Ω(n log n) bits for universal maximal matching algorithms, and a lower bound in time of Ω(e) moves for universal and cautious 1-maximal matching algorithms. A side contribution of our result is the optimality in both time and space of the self-stabilizing 1-maximal matching algorithm of Inoue et al. [8].