Popular matchings in the capacitated house allocation problem

  • Authors:

  • David F. Manlove;Colin T. S. Sng

  • Affiliations:

  • Department of Computing Science, University of Glasgow, Glasgow, UK;Department of Computing Science, University of Glasgow, Glasgow, UK

  • Venue:
  • ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
  • Year:
  • 2006

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Abstract

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' such that the number of agents who prefer their allocation in M' to that in M exceeds the number of 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 CHA 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. For the case where preference lists may contain ties, we give an O(√Cn1)+m) algorithm for the analogous problem.