On the Approximability of the Stable Matching Problem with Ties of Constant Size up to the Integrality Gap

05/11/2020

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by   Jochen Koenemann, et al.

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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.