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)

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 Robert
• 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.

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	Computing Science