An Equitable Solution to the Stable Marriage Problem

A stable marriage problem (SMP) of size n involves n men and n women, each of whom has ordered members of the opposite gender by descending preferability. A solution is a perfect matching among men and women, such that there exists no pair who prefer each other to their current spouses. The problem was formulated in 1962 by Gale and Shapley, who showed that any instance can be solved in polynomial time, and has attracted interest due to its application to any two-sided market. Still, the solution obtained by the Gale-Shapley algorithm is favorable to one side. Gusfield and Irving introduced the equitable stable marriage problem (ESMP), which calls for finding a stable matching that minimizes the distance between men´s and women´s sum-of-rankings of their spouses. Unfortunately, ESMP is strongly NP-hard, approximation algorithms therefor are impractical, while even proposed heuristics may run for an unpredictable number of iterations. We propose a novel, deterministic approach that treats both genders equally, while eschewing an exhaustive exploration of the space of all stable matchings. Our thorough experimental study shows that, in contrast to previous proposals, our method not only achieves high-quality solutions, but also terminates efficiently and repeatably on all tested large problem instances.