Part C project : Stable matchings Supervisor : James Martin Stable marriage
نویسنده
چکیده
The “stable marriage” problem is often described as follows. There are n men and n women; each of the men has an order of preference on the women, and each of the women has an order of preference on the men. A “matching” of the people into n man-woman pairs is said to be unstable if there exist some man and some woman who both prefer each other to their partner in the matching. If there is no such pair, the matching is stable. Does such a stable matching exist? This is a non-trivial question. Gale and Shapley [3] gave an algorithm which finds one. One version is as follows:
منابع مشابه
Part C project : Stable matchings Supervisor :
The “stable marriage” problem is often described as follows. There are n men and n women; each of the men has an order of preference on the women, and each of the women has an order of preference on the men. A “matching” of the people into n man-woman pairs is said to be unstable if there exist some man and some woman who both prefer each other to their partner in the matching. If there is no s...
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In this paper, we consider the communication complexity of protocols that compute stable matchings. We work within the context of Gale and Shapley’s original stable marriage problem[3]: n men and n women each privately hold a total and strict ordering on all of the members of the opposite gender. They wish to collaborate in order to find a stable matching—a pairing of the men and women such tha...
متن کاملThe structure of stable marriage with indifference
We consider the stable marriage problem where participants are permitted to express indifference in their preference lists (i.e., each list can be partially ordered). We prove that, in an instance where indifference takes the form of ties, the set of strongly stable matchings forms a distributive lattice. However, we show that this lattice structure may be absent if indifference is in the form ...
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تاریخ انتشار 2013