Popular Matchings in the Capacitated House Allocation Problem

  • David F. Manlove
  • Colin T. S. Sng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4168)


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 \(O(\sqrt{C}n_1+m)\) 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.


Bipartite Graph Maximum Match Preference List Strict Order Bipartite Match 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • David F. Manlove
    • 1
  • Colin T. S. Sng
    • 1
  1. 1.Department of Computing ScienceUniversity of GlasgowGlasgowUK

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