Popular Matchings in the Weighted Capacitated House Allocation Problem

Sng, C. T.S. and Manlove, D. F. (2007) Popular Matchings in the Weighted Capacitated House Allocation Problem. In: Algorithms and Complexity in Durham 2007: Proceedings of the Third ACiD Workshop, Durham, UK, 17-19 Sep 2007, pp. 129-140. ISBN 9781904987550

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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 O( √ Cn1 + m) 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:Conference Proceedings
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Manlove, Professor David
Authors: Sng, C. T.S., and Manlove, D. F.
College/School:College of Science and Engineering > School of Computing Science
ISBN:9781904987550
Copyright Holders:Copyright © 2007 The Authors
First Published:First published in Algorithms and Complexity in Durham 2007: Proceedings of the Third ACiD Workshop: 129-140
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
436361MATCH-UP - matching under preferences - algorithms and complexityRobert IrvingEngineering and Physical Sciences Research Council (EPSRC)EP/E011993/1COM - COMPUTING SCIENCE