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

Authors:
T. Hayashi;Y. Hata;Y. Ishida
Affiliations:
Department of Computer Science of Engineering, Toyohashi University of Technology, Aichi, Japan 441-8580;Department of Computer Science of Engineering, Toyohashi University of Technology, Aichi, Japan 441-8580;Department of Computer Science of Engineering, Toyohashi University of Technology, Aichi, Japan 441-8580
Venue:
Artificial Life and Robotics
Year:
2012

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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.