Improved Approximation of the Stable Marriage Problem

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

• Type: Conference
• Year: 2003
• Where: ESA
• Authors: Magnús M. Halldórsson, Kazuo Iwama, Shuichi Miyazaki, Hiroki Yanagisawa
• Keywords: ESA 2003, Maximal Matching, Stable Marriage Problem, Stable Matching