Theory of Computing Systems

, Volume 59, Issue 4, pp 683–699 | Cite as

Stable Marriage with General Preferences

  • Linda Farczadi
  • Konstantinos Georgiou
  • Jochen Könemann
Article

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.

Keywords

Stable marriage Cyclic stable marriage Matching NP-completeness 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Linda Farczadi
    • 1
  • Konstantinos Georgiou
    • 2
  • Jochen Könemann
    • 3
  1. 1.École Polytechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.Ryerson UniversityTorontoCanada
  3. 3.University of WaterlooWaterlooCanada

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