The Hospitals / Residents Problem with Couples: Complexity and Integer Programming Models

  • Péter Biró
  • David F. Manlove
  • Iain McBride
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8504)


The Hospitals / Residents problem with Couples (hrc) is a generalisation of the classical Hospitals / Residents problem (hr) that is important in practical applications because it models the case where couples submit joint preference lists over pairs of (typically geographically close) hospitals. In this paper we give a new NP-completeness result for the problem of deciding whether a stable matching exists, in highly restricted instances of hrc, and also an inapproximability bound for finding a matching with the minimum number of blocking pairs in equally restricted instances of hrc. Further, we present a full description of the first Integer Programming model for finding a maximum cardinality stable matching in an instance of hrc and we describe empirical results when this model applied to randomly generated instances of hrc.


Stable Match Maximum Cardinality Integer Program Formulation Preference List Joint Assignment 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Péter Biró
    • 1
  • David F. Manlove
    • 2
  • Iain McBride
    • 2
  1. 1.Institute of Economics, Research Centre for Economic and Regional StudiesHungarian Academy of SciencesBudapestHungary
  2. 2.School of Computing ScienceUniversity of GlasgowGlasgowUK

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