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A Heuristic Repair Algorithm for the Hospitals/Residents Problem with Ties

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Artificial Intelligence and Soft Computing (ICAISC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13588))

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Abstract

The Hospitals/Residents problem with Ties is a many-to-one stable matching problem and it has several practical applications. In this paper, we present a heuristic repair algorithm to find a stable matching with maximal size for this problem. Our approach is to apply a random-restart algorithm used commonly to deal with constraint satisfaction problems. At each iteration, our algorithm finds and removes the conflicted pairs in terms of preference ranks between hospitals and residents to improve rapidly the stability of the matching. Experimental results show that our approach is efficient in terms of execution time and solution quality for the problem of large sizes.

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References

  1. Canadian resident matching service (CaRMS). http://www.carms.ca/

  2. 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 (June 2014)

    Google Scholar 

  3. Gale, D., Shapley, L.S.: College admissions and the stability of marriage. Am. Math. Mon. 9(1), 9–15 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  4. 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 (August 2010)

    Google Scholar 

  5. 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)

    Article  MathSciNet  MATH  Google Scholar 

  6. 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 (July 2002)

    Google Scholar 

  7. Irving, R.W.: Matching medical students to pairs of hospitals: A new variation on a well-known theme. In: Proceedings of ESA 1998: the 6th Annual European Symposium, Venice, Italy, pp. 381–392 (August 1998)

    Google Scholar 

  8. 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 (July 2000)

    Google Scholar 

  9. 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

    Chapter  Google Scholar 

  10. Iwama, K., Miyazaki, S., Morita, Y., Manlove, D.: Stable marriage with incomplete lists and ties. In: Proceedings of International Colloquium on Automata, Languages, and Programming, Prague, Czech Republic, pp. 443–452 (July 1999)

    Google Scholar 

  11. Király, Z.: Linear time local approximation algorithm for maximum stable marriage. Algorithms 6(1), 471–484 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kwanashie, A., Manlove, D.F.: An integer programming approach to the hospitals/residents problem with ties. In: Proceedings of the International Conference on Operations Research, pp. 263–269. Erasmus University Rotterdam (September 2013)

    Google Scholar 

  13. Manlove, D.: Algorithmics of Matching Under Preferences, vol. 2. World Scientific (2013)

    Google Scholar 

  14. Manlove, D.F., Irving, R.W., Iwama, K., Miyazaki, S., Morita, Y.: Hard variants of stable marriage. Theoret. Comput. Sci. 276(1–2), 261–279 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  15. Manlove, D.F., McBride, I., Trimble, J.: “Almost-stable" matchings in the hospitals / residents problem with couples. Constraints 22(1), 50–72 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  16. 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, UK (April 2015)

    Google Scholar 

  17. Munera, D., Diaz, D., Abreu, S., Rossi, F., Saraswat, V., Codognet, P.: Solving hard stable matching problems via local search and cooperative parallelization. In: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, Austin, Texas, pp. 1212–1218 (January 2015)

    Google Scholar 

  18. 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)

    Article  Google Scholar 

  19. Russel, S., Norvig, P.: Artificial Intelligence: A Modern Approach, 3rd edn. Prentice Hall Press, Upper Saddle River (2009)

    Google Scholar 

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Authors and Affiliations

  1. School of Engineering and Technology, Vinh University, Vinh City, Vietnam

    Son Thanh Cao, Le Quoc Anh & Hoang Huu Viet

Authors
  1. Son Thanh Cao
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  2. Le Quoc Anh
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  3. Hoang Huu Viet
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Corresponding author

Correspondence to Hoang Huu Viet .

Editor information

Editors and Affiliations

  1. Systems Research Institute of the Polish Academy of Sciences, Warsaw, Poland

    Leszek Rutkowski

  2. Częstochowa University of Technology, Częstochowa, Poland

    Rafał Scherer

  3. Częstochowa University of Technology, Częstochowa, Poland

    Marcin Korytkowski

  4. University of Alberta, Edmonton, AB, Canada

    Witold Pedrycz

  5. AGH University of Science and Technology, Kraków, Poland

    Ryszard Tadeusiewicz

  6. University of Louisville, Louisville, KY, USA

    Jacek M. Zurada

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Cao, S.T., Anh, L.Q., Viet, H.H. (2023). 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) Artificial Intelligence and Soft Computing. ICAISC 2022. Lecture Notes in Computer Science(), vol 13588. Springer, Cham. https://doi.org/10.1007/978-3-031-23492-7_29

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  • DOI: https://doi.org/10.1007/978-3-031-23492-7_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-23491-0

  • Online ISBN: 978-3-031-23492-7

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