Abstract
This paper proposes a local search algorithm to find the egalitarian and the sex-equal stable matchings in the stable marriage problem. Based on the dominance relation of stable matchings from the men’s point of view, our approach discovers the egalitarian and the sex-equal stable matchings from the man-optimal stable matching. By employing a breakmarriage strategy to find stable neighbor matchings of the current stable matching and moving to the best neighbor matching, our local search finds the solutions while moving towards the woman-optimal stable matching. Simulations show that our proposed algorithm is efficient for the stable marriage problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abraham, D.J., Irving, R.W., Manlove, D.F.: The student-project allocation problem. In: Proceedings of the 14th International Symposium, pp. 474–484. Kyoto, Japan, December 2003
Fleiner, T., Irving, R.W., Manlove, D.F.: Efficient algorithms for generalized stable marriage and roommates problems. Theor. Comput. Sci. 381(1–3), 162–176 (2007)
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 approaches in stable matching problems. Algorithms 6(1), 591–617 (2013)
Gusfield, D.: Three fast algorithms for four problems in stable marriage. SIAM J. Comput. 16(1), 111–128 (1987)
Gusfield, D., Irving, R.W.: The Stable Marriage Problem: Structure and Algorithms. MIT Press, Cambridge (1989)
Irving, R.W.: An efficient algorithm for the “stable roommates” problem. J. Algorithms 6(1), 577–595 (1985)
Irving, R.W., Leather, P.: The complexity of counting stable marriages. SIAM J. Comput. 15(3), 655–667 (1986)
Iwama, K., Miyazaki, S., Yanagisawa, H.: Approximation algorithms for the sex-equal stable marriage problem. ACM Trans. Algorithms 7(1), 2:1–2:17 (2010)
McVitie, D.G., Wilson, L.B.: The stable marriage problem. Commun. ACM 14(7), 486–490 (1971)
Nakamura, M., Onaga, K., Kyan, S., Silva, M.: Genetic algorithm for sex-fairstable marriage problem. In: 1995 IEEE International Symposium on Circuits and Systems, ISCAS 1995, vol. 1, pp. 509–512. Seattle, WA, April 1995
Roth, A.E.: The evolution of the labor market for medical interns and residents: a case study in game theory. J. Polit. Econ. 92(6), 991–1016 (1984)
Russel, S., Norvig, P.: Artificial Intelligence: A Modern Approach, 3rd edn. Pearson Education, Upper Saddle River (2010)
Vien, N.A., Viet, N.H., Kim, H., Lee, S., Chung, T.: Ant colony based algorithm for stable marriage problem. Adv. Innov. Syst. Comput. Sci. Softw. Eng. 1, 457–461 (2007)
Acknowledgements
The authors are grateful to the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2014R1A1A2057735), IITP (2015-(R0134-15-1033)) and the Kyung Hee University in 2013 [KHU-20130439].
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Viet, H.H., Trang, L.H., Lee, S., Chung, T. (2016). An Empirical Local Search for the Stable Marriage Problem. In: Booth, R., Zhang, ML. (eds) PRICAI 2016: Trends in Artificial Intelligence. PRICAI 2016. Lecture Notes in Computer Science(), vol 9810. Springer, Cham. https://doi.org/10.1007/978-3-319-42911-3_46
Download citation
DOI: https://doi.org/10.1007/978-3-319-42911-3_46
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42910-6
Online ISBN: 978-3-319-42911-3
eBook Packages: Computer ScienceComputer Science (R0)