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Polynomially tractable cases in the popular roommates problem

Author

Listed:
  • Erika Bérczi-Kovács

    (Eötvös Loránd University, Hungary)

  • Ágnes Cseh

    (University of Bayreuth, Germany)

  • Kata Kosztolányi

    (Eötvös Loránd University, Hungary)

  • Attila Mályusz

    (University of Freiburg, Germany)

Abstract

The input of the popular roommates problem consists of a graph G = (V, E) and for each vertex v in V, strict preferences over the neighbors of v. Matching M is more popular than M' if the number of vertices preferring M to M' is larger than the number of vertices preferring M' to M. A matching M is called popular if there is no matching M' that is more popular than M. Faenza et al. (2019) and Gupta et al. (2021) proved that determining the existence of a popular matching in a popular roommates instance is NP-complete. In this paper we identify a class of instances that admit a polynomial-time algorithm for the problem. We also test these theoretical findings on randomly generated instances to determine the existence probability of a popular matching in them.

Suggested Citation

  • Erika Bérczi-Kovács & Ágnes Cseh & Kata Kosztolányi & Attila Mályusz, 2025. "Polynomially tractable cases in the popular roommates problem," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 10(1), pages 67-95, December.
    • Handle: RePEc:jmi:articl:jmi-v10i1a3
    DOI: 10.22574/jmid.2025.12.003
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    JEL classification:

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

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