Popular matchings

Abraham, D.J., Irving, R.W., Mehlhorn, K. and Telikepalli, K. (2005) Popular matchings. In: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Vancouver, British Columbia, Canada, 23-25 January 2005, pp. 424-432. ISBN 0898715857

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Abstract

We consider the problem of matching a set of applicants to a set of posts, where each applicant has a preference list, ranking a non-empty subset of posts in order of preference, possibly involving ties. We say that a matching M is popular if there is no matching M' such that the number of applicants preferring M' to M exceeds the number of applicants preferring M to M'. In this paper, we give the first polynomial-time algorithms to determine if an instance admits a popular matching, and to find a largest such matching, if one exists. For the special case in which every preference list is strictly ordered (i.e. contains no ties), we give an O(n+m) time algorithm, where n is the total number of applicants and posts, and m is the total length of all the preference lists. For the general case in which preference lists may contain ties, we give an O(√nm) time algorithm, and show that the problem has equivalent time complexity to the maximum-cardinality bipartite matching problem.

Item Type:Conference Proceedings
Additional Information:© ACM, 2005. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in First published in Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (2005).
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Irving, Dr Rob
Authors: Abraham, D.J., Irving, R.W., Mehlhorn, K., and Telikepalli, K.
Subjects:Q Science > QA Mathematics > QA76 Computer software
College/School:College of Science and Engineering > School of Computing Science
Publisher:ACM Press
ISBN:0898715857
Copyright Holders:Copyright © 2005 ACM Press
First Published:First published in Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher.

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