Approximating Stable Matchings with Ties of Bounded Size.

Finding a stable matching is one of the central problems in algorithmic game theory. If participants are allowed to have ties and incomplete lists, computing a stable matching of maximum cardinality is known to be NP-hard. In this paper we present a (3L - 2)/(2L - 1)-approximation algorithm for the stable matching problem with ties of size at most L and incomplete preferences. Our result matches the known lower bound on the integrality gap for the associated LP formulation.