A generalization of the stable matching problem

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Abstract

It is known that there may not exist any stable matching for a given instance of the stable roommates problem. A stable partition is a structure that generalizes the notion of a stable matching; Tan (1991) proved that every instance of the stable roommates problem contains at least one such structure. In this paper we propose a new algorithm for finding a stable partition, and hence a new algorithm for finding a stable matching if one exists. Our algorithm processes the problem dynamically as long as certain relative preference orders are maintained. Some theoretical results about stable partitions are also presented.

Keywords

Stable roommates problem
Stable matching
Stable partition
Algorithm

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This research was supported by the National Science Council of the Republic of China under grant NSC 81-0408-E-009-03.