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Approximating Stable Matchings with Ties of Bounded Size (2005.05228v2)
Published 11 May 2020 in cs.GT and math.OC
Abstract: Finding a stable matching is one of the central problems in algorithmic game theory. If participants are allowed to have ties and incomplete preferences, 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 lists. Our result matches the known lower bound on the integrality gap for the associated LP formulation.