Encyclopedia of Algorithms

2008 Edition
| Editors: Ming-Yang Kao

Hospitals/Residents Problem

1962; Gale, Shapley
  • David F. Manlove
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_180

Keywords and Synonyms

College admissions problem ; University admissions problem; Stable admissions problem ; Stable assignment problem ; Stable b-matching problem      

Problem Definition

An instance I of the Hospitals/Residents problem (HR) [5,6,14] involves a set \( { R = \{r_1,\dots,r_n\} } \)

This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    Abdulkadiroğlu, A., Pathak, P.A., Roth, A.E.: The New York City high school match. Am. Economic. Rev. 95(2), 364–367 (2006)CrossRefGoogle Scholar
  2. 2.
    Abraham, D.J., Irving, R.W., Manlove, D.F.: Two algorithms for the Student-Project allocation problem. J. Discret. Algorithms 5(1), 73–90 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Baïou, M., Balinski, M.: Student admissions and faculty recruitment. Theor. Comput. Sci. 322(2), 245–265 (2004)zbMATHCrossRefGoogle Scholar
  4. 4.
    Bansal, V., Agrawal, A., Malhotra, V.S.: Stable marriages with multiple partners: efficient search for an optimal solution. In: Proceedings of ICALP '03: the 30th International Colloquium on Automata, Languages and Programming. Lecture Notes in Computer Science, vol. 2719, pp. 527–542. Springer, Berlin (2003)Google Scholar
  5. 5.
    Gale, D., Shapley, L.S.: College admissions and the stability of marriage. Am. Math. Month. 69, 9–15 (1962)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Gusfield, D., Irving, R.W.: The Stable Marriage Problem: Structure and Algorithms. MIT Press, Cambridge (1989)zbMATHGoogle Scholar
  7. 7.
    Irving, R.W., Manlove, D.F., Scott, S.: The Hospitals/Residents problem with Ties. In: Proceedings of SWAT 2000: the 7th Scandinavian Workshop on Algorithm Theory. Lecture Notes in Computer Science, vol. 1851, pp. 259–271. Springer, Berlin (2000)Google Scholar
  8. 8.
    Irving, R.W., Manlove, D.F., Scott, S.: Strong stability in the Hospitals/Residents problem. In: Proceedings of STACS 2003: the 20th Annual Symposium on Theoretical Aspects of Computer Science. Lecture Notes in Computer Science, vol. 2607, pp. 439–450. Springer, Berlin (2003)Google Scholar
  9. 9.
    Irving, R.W., Scott, S.: The stable fixtures problem – a many-to-many extension of stable roommates. Discret. Appl. Math. 155, 2118–2129 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Kavitha, T., Mehlhorn, K., Michail, D., Paluch, K.: Strongly stable matchings in time O(nm) and extension to the Hospitals-Residents problem. In: Proceedings of STACS 2004: the 21st International Symposium on Theoretical Aspects of Computer Science. Lecture Notes in Computer Science, vol. 2996, pp. 222–233. Springer, Berlin (2004)Google Scholar
  11. 11.
    Malhotra, V.S.: On the stability of multiple partner stable marriages with ties. In: Proceedings of ESA '04: the 12th Annual European Symposium on Algorithms. Lecture Notes in Computer Science, vol. 3221, pp. 508–519. Springer, Berlin (2004)Google Scholar
  12. 12.
    Romero-Medina, A.: Implementation of stable solutions in a restricted matching market. Rev. Economic. Des. 3(2), 137–147 (1998)Google Scholar
  13. 13.
    Ronn, E.: NP-complete stable matching problems. J. Algorithms 11, 285–304 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Roth, A.E., Sotomayor, M.A.O.: Two-sided matching: a study in game-theoretic modeling and analysis. Econometric Society Monographs, vol. 18. Cambridge University Press, Cambridge, UK (1990)Google Scholar
  15. 15.
    Scott, S.: A study of stable marriage problems with ties. Ph. D. thesis, University of Glasgow, Dept. Comput. Sci. (2005)Google Scholar
  16. 16.
    http://www.nrmp.org/ (National Resident Matching Program website)
  17. 17.
    http://www.carms.ca (Canadian Resident Matching Service website)
  18. 18.
    http://www.nes.scot.nhs.uk/sfas/ (Scottish Foundation Allocation Scheme website)
  19. 19.
    http://www.jrmp.jp (Japan Resident Matching Program website)

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • David F. Manlove
    • 1
  1. 1.Department of Computing ScienceUniversity of GlasgowGlasgowUK