Abstract
A stable marriage problem of sizen involvesn men andn women each with a strict preference ordering over all the members of the opposite sex. A solution, called a stable matching, matches the men and women so that no man and woman both prefer each other to their respective partners. The sex-equal stable marriage problem posed by Gusfield and Irving [5] is that of finding a stable matching with the property that the sum of the men’s scores is as close as possible to that of the women’s. This paper shows that the sex-equal stable marriage problem is NP-hard even if each person’s scores coincide with his rankings.
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Kato, A. Complexity of the sex-equal stable marriage problem. Japan J. Indust. Appl. Math. 10, 1–19 (1993). https://doi.org/10.1007/BF03167200
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DOI: https://doi.org/10.1007/BF03167200