Popular matchings: structure and algorithms

McDermid, E. and Irving, R.W. (2009) Popular matchings: structure and algorithms. Lecture Notes in Computer Science, 5609, pp. 506-515. (doi:10.1007/978-3-642-02882-3_50)

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Publisher's URL: http://dx.doi.org/10.1007/978-3-642-02882-3_50

Abstract

An instance of the popular matching problem (POP-M) consists of a set of applicants and a set of posts. Each applicant has a preference list that strictly ranks a subset of the posts. A matching M of applicants to posts is popular if there is no other matching M' such that more applicants prefer M' to M than prefer M to M'. This paper provides a characterization of the set of popular matchings for an arbitrary POP-M instance in terms of a structure called the switching graph, a directed graph computable in linear time from the preference lists. We show that the switching graph can be exploited to yield efficient algorithms for a range of associated problems, including the counting and enumeration of the set of popular matchings and computing popular matchings that satisfy various additional optimality criteria. Our algorithms for computing such optimal popular matchings improve those described in a recent paper by Kavitha and Nasre.

Item Type:Articles
Additional Information:The original publication is available at www.springerlink.com
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Irving, Dr Rob
Authors: McDermid, E., and Irving, R.W.
Subjects:Q Science > QA Mathematics > QA75 Electronic computers. Computer science
College/School:College of Science and Engineering > School of Computing Science
Research Group:FATA
Journal Name:Lecture Notes in Computer Science
Publisher:Springer
ISSN:1611-3349
Copyright Holders:Copyright © 2009 Springer
First Published:First published in Lecture Notes in Computer Science 5609:506-515
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/E011993/1Computing Science