Abstract
The Hospitals/Residents with Ties Problem is a many-one stable matching problem, in which residents need to be assigned to hospitals to meet their constraints. In this paper, we propose a simple heuristic algorithm but solve this problem efficiently. Our algorithm starts from an empty matching and gradually builds up a maximum stable matching of residents to hospitals. At each iteration, we propose a heuristic function to choose the best hospital for an active resident to form a resident-hospital pair for the matching. If the chosen hospital overcomes its offered capacity, we propose another heuristic function to remove the worst resident among residents assigned to the hospital in the matching. Our algorithm returns a stable matching if it finds no active resident. Experimental results show that our algorithm is efficient in execution time and solution quality for solving the problem.
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References
Biró, P., Manlove, D.F., McBride, I.: The hospitals/residents problem with couples: complexity and integer programming models. In: Proceeding of SEA 2014: 13th International Symposium on Experimental Algorithms, Copenhagen, Denmark, pp. 10–21 (2014)
Cao, S.T., Anh, L.Q., Viet, H.H.: A heuristic repair algorithm for the hospitals/residents problem with ties. In: Rutkowski, L., Scherer, R., Korytkowski, M., Pedrycz, W., Tadeusiewicz, R., Zurada, J.M. (eds.) ICAISC 2022. LNCS, vol. 13588, pp. 340–352. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-23492-7_29
Gale, D., Shapley, L.S.: College admissions and the stability of marriage. Am. Math. Mon. 9(1), 9–15 (1962)
Gelain, M., Pini, M.S., Rossi, F., Venable, K.B., Walsh, T.: Local search for stable marriage problems with ties and incomplete lists. In: Proceedings of 11th Pacific Rim International Conference on Artificial Intelligence, Daegu, Korea, pp. 64–75 (2010)
Gelain, M., Pini, M.S., Rossi, F., Venable, K.B., Walsh, T.: Local search approaches in stable matching problems. Algorithms 6(4), 591–617 (2013)
Gent, I.P., Prosser, P.: An empirical study of the stable marriage problem with ties and incomplete lists. In: Proceedings of the 15th European Conference on Artificial Intelligence, Lyon, France, pp. 141–145 (2002)
Gusfield, D., Irving, R.W.: The Stable Marriage Problem: Structure and Algorithms. MIT Press Cambridge, New York (1989)
Irving, R.W.: Stable marriage and indifference. Discret. Appl. Math. 48, 261–272 (1974)
Irving, R.W., Manlove, D.F., Scott, S.: The hospitals/residents problem with ties. In: Proceedings of the 7th Scandinavian Workshop on Algorithm Theory, Bergen, Norway, pp. 259–271 (2000)
Irving, R.W., Manlove, D.F., Scott, S.: Strong stability in the hospitals/residents problem. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 439–450. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36494-3_39
Király, Z.: Linear time local approximation algorithm for maximum stable marriage. Algorithms 6(1), 471–484 (2013)
Kwanashie, A., Manlove, D.F.: An integer programming approach to the hospitals/residents problem with ties. In: Huisman, D., Louwerse, I., Wagelmans, A.P.M. (eds.) Operations Research Proceedings 2013. ORP, pp. 263–269. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-07001-8_36
Munera, D., Diaz, D., Abreu, S., Rossi, F., Saraswat, V., Codognet, P.: A local search algorithm for SMTI and its extension to HRT problems. In: Proceedings of the 3rd International Workshop on Matching Under Preferences, pp. 66–77. University of Glasgow (2015)
Irving, R.W., Manlove, D.F.: Finding large stable matchings. J. Exp. Algorithmics 14(1), 1–2 (2009)
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Cao, S.T., Thanh, L.V., Viet, H.H. (2024). Finding Maximum Weakly Stable Matchings for Hospitals/Residents with Ties Problem via Heuristic Search. In: Liu, T., Webb, G., Yue, L., Wang, D. (eds) AI 2023: Advances in Artificial Intelligence. AI 2023. Lecture Notes in Computer Science(), vol 14471. Springer, Singapore. https://doi.org/10.1007/978-981-99-8388-9_36
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DOI: https://doi.org/10.1007/978-981-99-8388-9_36
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