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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 comparator circuit value problem (CCVP) is CC-complete. In the stable marriage problem, there is an equal number of men and women. Each person ranks all members of the opposite sex. A matching between men and women is stable if there are no unpaired man and woman who prefer each other over their current partners. A stable matching always ...
Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis is a book on matching markets in economics and game theory, particularly concentrating on the stable marriage problem. It was written by Alvin E. Roth and Marilda Sotomayor , with a preface by Robert Aumann , [ 1 ] [ 2 ] and published in 1990 by the Cambridge University Press ...
Couples' rank order lists are processed simultaneously by the matching algorithm, which complicates the problem. In some cases there exists no stable solution (with stable defined the way it is in the simple case). In fact, the problem of determining whether there is a stable solution and finding it if it exists has been proven NP-complete. [27]
Agreements between young friends to marry later in life are a trope of American entertainment, [1] popularized in the film My Best Friend's Wedding, [2] [3] that also occur occasionally in life. [1] The stable marriage problem, and human matching more generally, is a problem of allocation.
Graphs of probabilities of getting the best candidate (red circles) from n applications, and k/n (blue crosses) where k is the sample size. 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.
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 ...