The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
Stable marriage and indifference
CO89 Selected papers of the conference on Combinatorial Optimization
Semiring-based constraint satisfaction and optimization
Journal of the ACM (JACM)
The Hospitals/Residents Problem with Ties
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Matching Medical Students to Pairs of Hospitals: A New Variation on a Well-Known Theme
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Journal of Artificial Intelligence Research
Male optimality and uniqueness in stable marriage problems with partial orders
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
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The stable marriage problem has a wide variety of practical applications, including matching resident doctors to hospitals, and students to schools. In the classical stable marriage problem, both men and women express a strict order over the members of the other sex. Here we consider a more realistic case, where both men and women can express their preferences via partial orders, i.e., by allowing ties and incomparability. This may be useful, for example, when preferences are elicited via compact preference representations like soft constraint or CP-nets that produce partial orders, as well as when preferences are obtained via multi-criteria reasoning. We study male optimality and uniqueness of stable marriages in this setting. Male optimality gives priority to one gender over the other, while uniqueness means that the solution is optimal, since it is as good as possible for all the participating agents. Uniqueness of solution is also a barrier against manipulation. We give an algorithm to find stable marriages that are male optimal. Moreover, we give sufficient conditions on the preferences (that are also necessary in some special case), that occur often in real-life scenarios, which guarantee the uniqueness of a stable marriage.