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)

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: Irving, Dr Robert and Manlove, Professor David
• 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

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
43636	1	MATCH-UP - matching under preferences - algorithms and complexity	Robert Irving	Engineering & Physical Sciences Research Council (EPSRC)	EP/E011993/1	COM - COMPUTING SCIENCE