First-Order and Second-Order Model Counting Meet Stable Marriages, Stable Roommates, and Stable Diners

Václav Kůla, Jan Tóth, Yuanhong Wang, Yuyi Wang, Ondrej Kuzelka

Keywords: stable matching, first-order logic

Abstract: We study the computational complexity of counting variants of classical stable matching problems, including the stable marriage, stable roommates, and stable seating arrangement problems. While these counting problems are generally intractable, we show that many become tractable when the agents’ preferences are drawn from only $k$ distinct classes. Our positive results build on recent advances in first-order and second-order model counting from the finite model theory literature. In particular, we demonstrate how these tools both extend recent positive results and resolve an open question about stable seating arrangements posed by Berriaud, Constantinescu, and Wattenhofer (Stable Dinner Party Seating Arrangements, WINE 2023).

Area: Game Theory and Economic Paradigms (GTEP)

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Submission Number: 1444