Counting Popular Matchings in House Allocation Problems

  • Rupam Acharyya
  • Sourav Chakraborty
  • Nitesh Jha
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8476)


We study the problem of counting the number of popular matchings in a given instance. McDermid and Irving gave a poly-time algorithm for counting the number of popular matchings when the preference lists are strictly ordered. We first consider the case of ties in preference lists. Nasre proved that the problem of counting the number of popular matching is #P-hard when there are ties. We give an FPRAS for this problem.

We then consider the popular matching problem where preference lists are strictly ordered but each house has a capacity associated with it. We give a switching graph characterization of popular matchings in this case. Such characterizations were studied earlier for the case of strictly ordered preference lists (McDermid and Irving) and for preference lists with ties (Nasre). We use our characterization to prove that counting popular matchings in capacitated case is #P-hard.


Bipartite Graph Outgoing Edge Maximum Match Stable Matchings Incoming Edge 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Rupam Acharyya
    • 1
  • Sourav Chakraborty
    • 1
  • Nitesh Jha
    • 1
  1. 1.Chennai Mathematical InstituteChennaiIndia

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