Years and Authors of Summarized Original Work
1987; Irving, Leather, Gusfield
Problem Definition
The classical stable marriage problem (SM), first studied by Gale and Shapley [5], is introduced in Stable Marriage. An instance of SM comprises a set \(\mathcal{M} =\{ m_{1},\ldots ,m_{n}\}\) of n men and a set \(\mathcal{W} =\{ w_{1},\ldots ,w_{n}\}\) of n women and for each person a preference list, which is a total order over the members of the opposite sex. A man’s (respectively woman’s) preference list indicates his (respectively her) strict order of preference over the women (respectively men). A matching M is a set of n man-woman pairs in which each person appears exactly once. If the pair (m, w) is in the matching M, then m and w are partners in M, denoted by w = M(m) and m = M(w). Matching M is stable if there is no man m and woman w such that m prefers w to M(m) and w prefers m to M(w).
The key result established in [5] is that at least one stable matching exists for every...
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Irving, R.W. (2016). Optimal Stable Marriage. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_271
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DOI: https://doi.org/10.1007/978-1-4939-2864-4_271
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