A Max-Min Conflict Algorithm for the Stable Marriage Problem.

In this paper we present a max-min conflict algorithm to find a stable matching rather than the man- and woman-optimal matchings for the stable marriage problem. We solve the problem in terms of a constraint satisfaction problem, i.e. find a complete assignment for men in which every man is assigned to a woman so that the assignment does not contain any blocking pairs. To do this, we apply a local search method in which a max-conflict heuristic is used to choose the man making the maximum number of blocking pairs in a matching, while a min-conflict heuristic is used to remove all the blocking pairs formed by the chosen man. Experiments showed that our algorithm is efficient for finding a stable matching of large stable marriage problems.