Popular Matchings in the Marriage and Roommates Problems

  • Péter Biró
  • Robert W. Irving
  • David F. Manlove
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6078)


Popular matchings have recently been a subject of study in the context of the so-called House Allocation Problem, where the objective is to match applicants to houses over which the applicants have preferences. A matching M is called popular if there is no other matching M′ with the property that more applicants prefer their allocation in M′ to their allocation in M. In this paper we study popular matchings in the context of the Roommates Problem, including its special (bipartite) case, the Marriage Problem. We investigate the relationship between popularity and stability, and describe efficient algorithms to test a matching for popularity in these settings. We also show that, when ties are permitted in the preferences, it is NP-hard to determine whether a popular matching exists in both the Roommates and Marriage cases.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Péter Biró
    • 1
  • Robert W. Irving
    • 1
  • David F. Manlove
    • 1
  1. 1.Department of Computing ScienceUniversity of GlasgowGlasgowUK

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