SMS: Stable Matching Algorithm using Skylines

Abstract

In this paper we show how skylines can be used to improve the stable matching algorithm with asymmetric preference sets for men and women. The skyline set of men (or women) in a dataset comprises of those who are not worse off in all the qualities in comparison to another man (or woman). We prove that if a man in the skyline set is matched with a woman in the skyline set, the resulting pair is stable. We design our algorithm, SMS, based on the above observation by running the matching algorithm in phases considering only the skyline sets. In addition to being efficient, SMS provides two important additional properties. The first is progressiveness where stable pairs are output without waiting for the entire algorithm to finish. The second is balance in quality between men versus women since the proposers are switched automatically between the sets. Empirical results show that SMS runs orders of magnitude faster than the original Gale-Shapley algorithm and produces better quality matchings.