The exchange-stable marriage problem

Cechlarova, K. and Manlove, D.F. (2005) The exchange-stable marriage problem. Discrete Applied Mathematics, 152(1-3), pp. 109-122. (doi:10.1016/j.dam.2005.06.003)

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Publisher's URL: http://dx.doi.org/10.1016/j.dam.2005.06.003

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.

Item Type:Articles
Keywords:Stable marriage problem; Stable roommates problem; Matching; Coalition-exchange-stable; Man-exchange-stable
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Manlove, Dr David
Authors: Cechlarova, K., and Manlove, D.F.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Computing Science
Research Group:Formal Analysis, Theory and Algorithms
Journal Name:Discrete Applied Mathematics
Publisher:Elsevier
ISSN:0166-218X
Copyright Holders:© 2005 Elsevier B.V.
First Published:First published in Discrete Applied Mathematics 152(1-3):109-122
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher.

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