On Stable Marriages and Greedy Matchings

Research on stable marriage problems has a long and mathematically rigorous history, while that of exploiting greedy matchings in combinatorial scientific computing is a younger and less developed research field. We consider the relationships between these two areas. In particular we show that several problems related to computing greedy matchings can be formulated as stable marriage problems and as a consequence several recently proposed algorithms for computing greedy matchings are in fact special cases of well known algorithms for the stable marriage problem.

However, in terms of implementations and practical scalable solutions on modern hardware, work on computing greedy matchings has made considerable progress. We show that due to this strong relationship many of these results are also applicable for solving stable marriage problems. This is further demonstrated by designing and testing efficient multicore as well as GPU algorithms for the stable marriage problem.