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A diagrammatic classification in a combinatorial problem: the case of the stable marriage problem

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Abstract

The stable marriage problem (SMP) is a combinatorial problem to find stable matching between n women and n men given a complete preference list of men over women and vice versa. An instance of the SMP can be expressed by a bipartite graph with multiple (weighted) edges. By rearranging the graph, we use a diagram that involves several constraints to visualize several symmetries. By the diagram, all instances of the size-three SMP (three women and three men) are classified. The classification may be supported by the fact that the same class has the same stable matching.

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References

  1. Gale D, Shapley LS (1962) College admissions and the stability of marriage Am Math Monthly 69:9–15

    Article  MathSciNet  MATH  Google Scholar 

  2. Gusfield D, Irving RW (1989) The stable marriage problem: structure and algorithm. MIT Press, London

    MATH  Google Scholar 

  3. Morizumi Y, Hayashi T, Ishida Y (2009) A network visualization of stable matching in the stable marriage problem. Proceedings of AROB

  4. Balinski M, Ratier G (1997) Of stable marriages and graphs, and strategy and polytopes. SIAM Rev 39:575–604

    Article  MathSciNet  MATH  Google Scholar 

  5. Nemoto T (2002) Handbook of applied mathematical programming (in Japanese). Asakura Syoten, pp 779–830

  6. Veklerov E (1989) On the decomposability of the stable marriage problem. BIT Numerical Math 29(1):41–46

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science of Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka, Tenpaku-cho, Toyohashi, Aichi, 441-8580, Japan

    T. Hayashi, Y. Hata & Y. Ishida

Authors
  1. T. Hayashi
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  2. Y. Hata
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  3. Y. Ishida
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Corresponding author

Correspondence to Y. Hata.

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Hayashi, T., Hata, Y. & Ishida, Y. A diagrammatic classification in a combinatorial problem: the case of the stable marriage problem. Artif Life Robotics 16, 575–579 (2012). https://doi.org/10.1007/s10015-011-0993-x

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  • DOI: https://doi.org/10.1007/s10015-011-0993-x

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