Popular matchings in the weighted capacitated house allocation problem

Authors:
Colin T. S. Sng;David F. Manlove
Affiliations:
Department of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK;Department of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK
Venue:
Journal of Discrete Algorithms
Year:
2010

Citing 11
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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(Cn"1+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, n"1 is the number of agents, and m is the total length of the agents' preference lists.