Computing at Glasgow University
Paper ID: 8240
DCS Tech Report Number: TR-2006-222

Popular Matchings in the Capacitated House Allocation Problem
Manlove,D.F. Sng,C.T.S.

Publication Type: Tech Report (internal)
Appeared in: DCS Technical Report Series
Page Numbers :
Publisher: Dept of Computing Science, University of Glasgow
Year: 2006

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_0 such that the number of agents who prefer their allocation in M_0 to that in M exceeds the number of agents who prefer their allocation in M to that in M_0. Here, we give an O(\sqrt{C}n_1+m) 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, n_1 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((\sqrt{C} + n_1)m) algorithm for the analogous problem.

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