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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 ...
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 ...
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 ...
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 Topics referred to by the same term This disambiguation page lists articles associated with the title Marriage problem .
By applying linear programming to the stable matching polytope, one can find the minimum or maximum weight stable matching. [1] Alternative methods for the same problem include applying the closure problem to a partially ordered set derived from the lattice of stable matchings, [6] or applying linear programming to the order polytope of this ...
WATCH: Sarah Michelle Gellar blames America's marriage woes on ‘disposable’ society. The actress said that "hard work" is the secret behind her 22-year union with Freddie Prinze Jr.
A series of interlocking economic, policy, civic, and cultural changes since the 1960s in America combined to create a perfect family storm for poor and working-class Americans.12 On the economic front, the move to a postindustrial economy in the 1970s made it more difficult for poor and working-class men to find and hold stable, decent-paying ...