Stable Marriage with General Preferences

Extended Abstract
  • Linda Farczadi
  • Konstantinos Georgiou
  • Jochen Könemann
Conference paper

DOI: 10.1007/978-3-662-44803-8_3

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8768)
Cite this paper as:
Farczadi L., Georgiou K., Könemann J. (2014) Stable Marriage with General Preferences. In: Lavi R. (eds) Algorithmic Game Theory. SAGT 2014. Lecture Notes in Computer Science, vol 8768. Springer, Berlin, Heidelberg

Abstract

We propose a generalization of the classical stable marriage problem. In our model, the preferences on one side of the partition are given in terms of arbitrary binary relations, which need not be transitive nor acyclic. This generalization is practically well-motivated, and as we show, encompasses the well studied hard variant of stable marriage where preferences are allowed to have ties and to be incomplete. As a result, we prove that deciding the existence of a stable matching in our model is NP-complete. Complementing this negative result we present a polynomial-time algorithm for the above decision problem in a significant class of instances where the preferences are asymmetric. We also present a linear programming formulation whose feasibility fully characterizes the existence of stable matchings in this special case. Finally, we use our model to study a long standing open problem regarding the existence of cyclic 3D stable matchings. In particular, we prove that the problem of deciding whether a fixed 2D perfect matching can be extended to a 3D stable matching is NP- complete, showing this way that a natural attempt to resolve the existence (or not) of 3D stable matchings is bound to fail.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Linda Farczadi
    • 1
  • Konstantinos Georgiou
    • 1
  • Jochen Könemann
    • 1
  1. 1.University of WaterlooWaterlooCanada

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