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2020•arXiv (Cornell University)Open access

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

Jochen Könemann, Kanstantsin Pashkovich, Natig Tofigzade

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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.

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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.

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Available 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.

Key concepts: Cardinality (data modeling), Matching (statistics), Combinatorics, Mathematics, Constant (computer programming), Approximation algorithm, Upper and lower bounds, Stable marriage problem

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On the Approximability of the Stable Matching Problem with Ties of Constant Size up to the Integrality Gap. — Research Paper | ScholarLens