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

Approximating Stable Matchings with Ties of Bounded Size