Improved approximation of the stable marriage problem

Abstract

The stable marriage problem has recently been studied in its general setting, where both ties and incomplete lists are allowed. It is NP-hard to find a stable matching of maximum size, while any stable matching is a maximal matching and thus trivially a factor two approximation. In this paper, we give the first nontrivial result for approximation of factor less than two. Our algorithm achieves an approximation ratio of 2/(1+L-2) for instances in which only men have ties of length at most L. When both men and women are allowed to have ties, we show a ratio of 13/7(< 1.858) for the case when ties are of length two. We also improve the lower bound on the approximation ratio to 21/19(> 1.1052). © Springer-Verlag 2003.