1987/07/01 by Robert W. Irving, Paul Leather, P.S.H. Leather +1 · 257 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Graph Theory Research #Algorithm #Combinatorics #Complexity and Algorithms in Graphs #Computer science #Economics #Game Theory and Voting Systems #Graph #Machine learning #Matching (statistics) #Mathematical optimization #Mathematics #Order (exchange) #Preference #Set (abstract data type) #Stability (learning theory) #Stable marriage problem #Statistics
paper · pdf · doi:10.1145/28869.28871
published in Journal of the ACM 34(3), 532-543 (Association for Computing Machinery)
openalex publication_date 1987/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
In an instance of size n of the stable marriage problem, each of n men and n women ranks the members of the opposite sex in order of preference. A stable matching is a complete matching of men and women such that no man and woman who are not partners both prefer each other to their actual partners under the matching. It is well known [2] that at least one stable matching exists for every stable marriage instance. However, the classical Gale-Shapley algorithm produces a marriage that greatly favors the men at the expense of the women, or vice versa. The problem arises of finding a stable matching that is optimal under some more equitable or egalitarian criterion of optimality. This problem was posed by Knuth [6] and has remained unsolved for some time. Here, the objective of maximizing the average (or, equivalently, the total) “satisfaction” of all people is used. This objective is achieved when a person's satisfaction is measured by the position of his/her partner in his/her preference list. By exploiting the structure of the set of all stable matchings, and using graph-theoretic methods, an O ( n 4 ) algorithm for this problem is derived.