In mathematics , economics , and computer science , the stable marriage problem also stable matching problem or SMP is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element. A matching is a bijection from the elements of one set to the elements of the other set. A matching is not stable if:. In other words, a matching is stable when there does not exist any match A , B which both prefer each other to their current partner under the matching. Given n men and n women, where each person has ranked all members of the opposite sex in order of preference, marry the men and women together such that there are no two people of opposite sex who would both rather have each other than their current partners.
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