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Popular Matchings in the Stable Marriage Problem

  • Chien-Chung Huang
  • Telikepalli Kavitha
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6755)

Abstract

The input is a bipartite graph \(G = (\mathcal{A}\cup\mathcal{B}, E)\) where each vertex \(u \in \mathcal{A}\cup\mathcal{B}\) ranks its neighbors in a strict order of preference. A matching M * is said to be popular if there is no matching M such that more vertices are better off in M than in M *. We consider the problem of computing a maximum cardinality popular matching in G. It is known that popular matchings always exist in such an instance G, however the complexity of computing a maximum cardinality popular matching was not known so far. In this paper we give a simple characterization of popular matchings when preference lists are strict and a sufficient condition for a maximum cardinality popular matching. We then show an O(mn 0) algorithm for computing a maximum cardinality popular matching in G, where m = |E| and \(n_0 = \min(|\mathcal{A}|,|\mathcal{B}|)\).

Keywords

Bipartite Graph Stable Match Maximum Cardinality Preference List Simple Characterization 
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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