The exchange-stable marriage problem

Authors:
Katarína Cechlárová;David F. Manlove
Affiliations:
Institute of Mathematics, P.J. Šafárik University, Faculty of Science, Jesenná 5, 041 54 Košice, Slovakia;Department of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK
Venue:
Discrete Applied Mathematics
Year:
2005

Citing 5
Cited 1

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The stable marriage problem: structure and algorithms
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Abstract

In this paper we consider instances of stable matching problems, namely the classical stable marriage (SM) and stable roommates (SR) problems and their variants. In such instances we consider a stability criterion that has recently been proposed, that of exchange-stability. In particular, we prove that ESM-the problem of deciding, given an SM instance, whether an exchange-stable matching exists-is NP-complete. This result is in marked contrast with Gale and Shapley's classical linear-time algorithm for finding a stable matching in an instance of SM. We also extend the result for ESM to the SR case. Finally, we study some variants of ESM under weaker forms of exchange-stability, presenting both polynomial-time solvability and NP-completeness results for the corresponding existence questions.