Popular Matchings in the Capacitated House Allocation Problem

Manlove, D.F. and Sng, C.T.S. (2006) Popular Matchings in the Capacitated House Allocation Problem. In: Proceedings of ESA 2006: the 14th Annual European Symposium on Algorithms, Zurich, Switzerland, 11-13 September 2006, pp. 492-503. ISBN 978-3-540-38875-3 (doi:10.1007/11841036_45)

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Publisher's URL: http://dx.doi.org/10.1007/11841036_45

Abstract

We consider the problem of finding a popular matching in the Capacitated House Allocation problem (CHA). An instance of CHA involves a set of agents and a set of houses. Each agent has a preference list in which a subset of houses are ranked in strict order, and each house may be matched to a number of agents that must not exceed its capacity. A matching M is popular if there is no other matching M′ such that the number of agents who prefer their allocation in M′ to that in M exceeds the number of agents who prefer their allocation in M to that in M′. Here, we give an O(√C+n1m) algorithm to determine if an instance of CHA admits a popular matching, and if so, to find a largest such matching, where C is the total capacity of the houses, n1 is the number of agents and m is the total length of the agents’ preference lists. For the case where preference lists may contain ties, we give an O(√Cn1+m) algorithm for the analogous problem.

Item Type:Conference Proceedings
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Manlove, Professor David
Authors: Manlove, D.F., and Sng, C.T.S.
Subjects:Q Science > QA Mathematics > QA75 Electronic computers. Computer science
College/School:College of Science and Engineering > School of Computing Science
Research Group:Formal Analysis, Theory and Algorithms
Journal Name:Lecture Notes in Computer Science
Publisher:Springer
ISSN:0302-9743
ISBN:978-3-540-38875-3
Copyright Holders:Copyright © 2006 Springer
First Published:First published in the Lecture Notes in Computer Science 4168:492-503
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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