Stable matching problems with exchange restrictions

We study variants of classical stable matching problems in which there is an additional requirement for a stable matching, namely that there should not be two participants who would prefer to exchange partners. The problem is motivated by the experience of real-world medical matching schemes that use stable matchings, where cases have arisen in which two participants discovered that each of them would prefer the other's allocation, a situation that is seen as unfair. Our main result is that the problem of deciding whether an instance of the classical stable marriage problem admits a stable matching, with the additional property that no two men would prefer to exchange partners, is NP-complete. This implies a similar result for more general problems, such as the hospitals/residents problem, the many-to-one extension of stable marriage. Unlike previous NP-hardness results for variants of stable marriage, the proof exploits the powerful algebraic structure underlying the set of all ...

• Type: Journal
• Year: 2008
• Where: JCO
• Authors: Robert W. Irving
• Keywords: Classical Stable Matching, JCO 2008, Stable Marriage, Stable Matchings