Abstract
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.
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This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 102.01-2017.09.
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Viet, H.H., Uyen, N.T., My, P.T., Cao, S.T., Trang, L.H. (2019). A Max-Min Conflict Algorithm for the Stable Marriage Problem. In: Ohara, K., Bai, Q. (eds) Knowledge Management and Acquisition for Intelligent Systems. PKAW 2019. Lecture Notes in Computer Science(), vol 11669. Springer, Cham. https://doi.org/10.1007/978-3-030-30639-7_5
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