A 3/2-approximation algorithm for general stable marriage

Abstract

In an instance of the stable marriage problem with ties and incomplete preference lists, stable matchings can have different sizes. It is APX-hard to compute a maximum cardinality stable matching, but there have recently been proposed polynomial-time approximation algorithms, with constant performance guarantees for both the general version of this problem, and for several special cases. Our contribution is to describe a 3/2-approximation algorithm for the general version of this problem, improving upon the recent 5/3-approximation algorithm of Király. Interest in such algorithms arises because of the problem's application to centralized matching schemes, the best known of which involve the assignment of graduating medical students to hospitals in various countries. © 2009 Springer Berlin Heidelberg.