Near-Popular Matchings in the Roommates Problem

  • Chien-Chung Huang
  • Telikepalli Kavitha
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6942)

Abstract

Our input is a graph G = (V, E) where each vertex ranks its neighbors in a strict order of preference. The problem is to compute a matching in G that captures the preferences of the vertices in a popular way. Matching M is more popular than matching M′ if the number of vertices that prefer M to M′ is more than those that prefer M′ to M. The unpopularity factor of M measures by what factor any matching can be more popular than M. We show that G always admits a matching whose unpopularity factor is O(log|V|) and such a matching can be computed in linear time. In our problem the optimal matching would be a least unpopularity factor matching - we show that computing such a matching is NP-hard. In fact, for any ε > 0, it is NP-hard to compute a matching whose unpopularity factor is at most 4/3 − ε of the optimal.

Keywords

Stable Match Satisfying Assignment Preference List Arbitrary Permutation Stable Partition 
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 2011

Authors and Affiliations

  • Chien-Chung Huang
    • 1
  • Telikepalli Kavitha
    • 2
  1. 1.Humboldt-Universität zu BerlinGermany
  2. 2.Tata Institute of Fundamental ResearchIndia

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