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)

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 <i>exchange-stability</i>. 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, Professor 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.