Popular matchings in the marriage and roommates problems

Biró, P., Irving, R. and Manlove, D.F. (2010) Popular matchings in the marriage and roommates problems. Lecture Notes in Computer Science, 6078, pp. 97-108. (doi:10.1007/978-3-642-13073-1_10)

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Publisher's URL: http://dx.doi.org/10.1007/978-3-642-13073-1_10

Abstract

Popular matchings have recently been a subject of study in the context of the so-called House Allocation Problem, where the objective is to match applicants to houses over which the applicants have preferences. A matching M is called popular if there is no other matching M′ with the property that more applicants prefer their allocation in M′ to their allocation in M. In this paper we study popular matchings in the context of the Roommates Problem, including its special (bipartite) case, the Marriage Problem. We investigate the relationship between popularity and stability, and describe efficient algorithms to test a matching for popularity in these settings. We also show that, when ties are permitted in the preferences, it is NP-hard to determine whether a popular matching exists in both the Roommates and Marriage cases.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Manlove, Dr David and Irving, Dr Robert
Authors: Biró, P., Irving, R., and Manlove, D.F.
Subjects:Q Science > QA Mathematics > QA75 Electronic computers. Computer science
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Lecture Notes in Computer Science
Publisher:Springer Berlin / Heidelberg
ISSN:0302-9743
Copyright Holders:Copyright © 2010 Springer
First Published:First published in Lecture Notes in Computer Science 6078:97-108
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
436361MATCH-UP - matching under preferences - algorithms and complexityRobert IrvingEngineering & Physical Sciences Research Council (EPSRC)EP/E011993/1COM - COMPUTING SCIENCE