Popular matchings in the weighted capacitated house allocation problem

Sng, C.T.S. and Manlove, D.F. (2010) Popular matchings in the weighted capacitated house allocation problem. Journal of Discrete Algorithms, 8(2), pp. 102-116. (doi:10.1016/j.jda.2008.11.008)

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Publisher's URL: http://dx.doi.org/10.1016/j.jda.2008.11.008

Abstract

We consider the problem of finding a popular matching in the Weighted Capacitated House Allocation problem (WCHA). An instance of WCHA involves a set of agents and a set of houses. Each agent has a positive weight indicating his priority, and a preference list in which a subset of houses are ranked in strict order. Each house has a capacity that indicates the maximum number of agents who could be matched to it. A matching M of agents to houses is popular if there is no other matching M′ such that the total weight of the agents who prefer their allocation in M′ to that in M exceeds the total weight of the agents who prefer their allocation in M to that in M′. Here, we give an [FORMULA] algorithm to determine if an instance of WCHA 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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Manlove, Professor David
Authors: Sng, C.T.S., 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:Journal of Discrete Algorithms
Publisher:Elsevier
ISSN:1570-8667
ISSN (Online):1570-8675
Published Online:24 July 2009
Copyright Holders:Copyright © 2010 Elsevier
First Published:First published in Journal of Discrete Algorithms 8(2):102-116
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
320021Algorithmics of Stable Matching Problems with IndifferenceDavid ManloveEngineering & Physical Sciences Research Council (EPSRC)GR/R84597/01Computing Science
436361MATCH-UP - matching under preferences - algorithms and complexityRobert IrvingEngineering & Physical Sciences Research Council (EPSRC)EP/E011993/1COM - COMPUTING SCIENCE