Computing at Glasgow University
Paper ID: 7098
DCS Tech Report Number: TR-2003-142

The Exchange-Stable Marriage Problem
Cechlarova,K. Manlove,D.F.

Publication Type: Tech Report (internal)
Appeared in: DCS Tech Report
Page Numbers :
Publisher: Dept of Computing Science, University of Glasgow
Year: 2003

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 constrast 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 a weaker form of exchange-stability, presenting both polynomial-time solvability and NP-completeness results for the corresponding existence questions.

Keywords: Stable Marriage problem; Exchange-stable matching; Man-exchange-stable matching; NP-completeness; Polynomial-time algorithm

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