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In a uniformly-random instance of the stable marriage problem with n men and n women, the average number of stable matchings is asymptotically . [6] In a stable marriage instance chosen to maximize the number of different stable matchings, this number is an exponential function of n. [7]
A stable matching always exists, and the algorithmic problem solved by the Gale–Shapley algorithm is to find one. [3] The stable matching problem has also been called the stable marriage problem, using a metaphor of marriage between men and women, and many sources describe the Gale–Shapley algorithm in terms of marriage proposals. However ...
The secretary problem demonstrates a scenario involving optimal stopping theory [1] [2] that is studied extensively in the fields of applied probability, statistics, and decision theory. It is also known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem.
Whereas the main stable-marriage problem is symmetric in the two sexes, the "hospitals/residents problem" is not; one seeks an 1-to-n relation rather than a 1-to-1 one. I am a bit bothered that the article feels the need to explicitly assign the role of metaphorical "women" to one of the sides in the asymmetric problem (though I am pleasantly ...
Secretary problem, also called the sultan's dowry or best choice problem, in optimal stopping theory; Stable marriage problem, the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element
1. A matching is called weakly stable unless there is a couple each of whom strictly prefers the other to his/her partner in the matching. Robert W. Irving [1] extended the Gale–Shapley algorithm as shown below to provide such a weakly stable matching in time, where n is the size of the stable marriage problem. Ties in the men and women's ...
The theorem has many applications. For example, for a standard deck of cards, dealt into 13 piles of 4 cards each, the marriage theorem implies that it is possible to select one card from each pile so that the selected cards contain exactly one card of each rank (Ace, 2, 3, ..., Queen, King). This can be done by constructing a bipartite graph ...
Stable marriage problem; Stable marriage with indifference; Stable matching polytope; Stable roommates problem; T. Two-Sided Matching This page was last edited on 26 ...