Paper ID: 8647
DCS Tech Report Number: TR2007254
Popular Matchings in the Weighted Capacitated House Allocation problem
Sng,C.T.S.
Manlove,D.F.
Publication Type:
Tech Report (internal)
Appeared in:
DCS Technical Report Series
Page Numbers :
Publisher: Dept of Computing Science, University of Glasgow
Year: 2007
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(\sqrt{C}n_{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.
