Improved Paths to Stability for the Stable Marriage Problem

Abstract

The stable marriage problem has wide applications in distributed computing such as the placement of virtual machines in a distributed system. The stable marriage problem requires one to find a marriage with no blocking pair. Given a matching that is not stable, Roth and Vande Vate have shown that there exists a sequence of matchings that leads to a stable matching in which each successive matching is obtained by satisfying a blocking pair. The sequence produced by Roth and Vande Vate’s algorithm is of length O(n3) where n is the number of men (and women). In this paper, we present an algorithm that achieves stability in a sequence of matchings of length O(n2). We also give an efficient algorithm to find the stable matching closest to the given initial matching under an appropriate distance function between matchings.