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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 ...
Envy-free matching – a relaxation of stable matching for many-to-one matching problems; Rainbow matching for edge colored graphs; Stable matching polytope; Lattice of stable matchings; Secretary problem (also called marriage problem) – deciding when to stop to obtain the best reward in a sequence of options
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 ...
Matchmaking is the process of pairing two or more people together, usually for the purpose of marriage, in which case the intermediary or matchmaker is also known as a marriage broker. Matchmaking may be done as a profession for a fee or it may be done by clergy.
This sort of arranged marriage, in theory, enabled the girl to escape poverty and the wealthy family to get free labor and a daughter-in-law. Zhaozhui was a related custom by which a wealthy family that lacked an heir would arrange marriage of a boy child from another family.
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Modern TU matching follows work by Shapley and Shubik (1971), who provided a TU equivalent of Gale and Shapley (1962), as well as Becker (1973) who applied TU matching to the marriage market. [2] Matching theory typically focuses on two-sided matching, where two types of workers are considered (e.g. men and women in the marriage market, firms ...
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