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Popular Edges and Dominant Matchings

Author

Listed:
  • Agnes Cseh

    (Institute of Economics, Research Centre for Economic and Regional Studies, Hungarian Academy of Sciences, and Corvinus University of Budapest)

  • Telikepalli Kavitha

    (Tata Institute of Fundamental Research, Mumbai, India)

Abstract

Given a bipartite graph G=(A[B;E) with strict preference lists and given an edge e 2 E, we ask if there exists a popular matching in G that contains e. We call this the popular edge problem. A matching M is popular if there is no matching M0 such that the vertices that preferM0 toM outnumber those that preferM toM0. It is known that every stable matching is popular; however G may have no stable matching with the edge e. In this paper we identify another natural subclass of popular matchings called “dominant matchings” and show that if there is a popular matching that contains the edge e, then there is either a stable matching that contains e or a dominant matching that contains e. This allows us to design a linear time algorithm for identifying the set of popular edges. When preference lists are complete, we show an O(n3) algorithm to find a popular matching containing a given set of edges or report that none exists, where n = jAj+jBj.

Suggested Citation

  • Agnes Cseh & Telikepalli Kavitha, 2017. "Popular Edges and Dominant Matchings," CERS-IE WORKING PAPERS 1725, Institute of Economics, Centre for Economic and Regional Studies.
    • Handle: RePEc:has:discpr:1725
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    File URL: http://econ.core.hu/file/download/mtdp/MTDP1725.pdf
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    References listed on IDEAS

    as
    1. Eric McDermid & Robert W. Irving, 2011. "Popular matchings: structure and algorithms," Journal of Combinatorial Optimization, Springer, vol. 22(3), pages 339-358, October.
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    More about this item

    Keywords

    popular matching; matching under preferences; dominant matching;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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