Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Hospitals/Residents Problem

  • David F. ManloveEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_180


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

Years and Authors of Summarized Original Work

1962; Gale, Shapley

Problem Definition

An instance I of the Hospitals/Residents problem (HR) [6, 7, 18] involves a set \(R =\{ r_{1},\ldots ,r_{n}\}\)


Matching Stability 
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Recommended Reading

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    Abdulkadiroǧlu A, Pathak PA, Roth AE (2005) The New York city high school match. Am Econ Rev 95(2):364–367CrossRefGoogle Scholar
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    Askalidis G, Immorlica N, Kwanashie A, Manlove DF, Pountourakis E (2013) Socially stable matchings in the Hospitals/Residents problem. In: Proceedings of the 13th Algorithms and Data Structures Symposium (WADS’13), London, Canada. Lecture Notes in Computer Science, vol 8037. Springer, pp 85–96Google Scholar
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    Baïou M, Balinski M (2004) Student admissions and faculty recruitment. Theor Comput Sci 322(2):245–265MathSciNetzbMATHCrossRefGoogle Scholar
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    Biró P, Klijn F (2013) Matching with couples: a multidisciplinary survey. Int Game Theory Rev 15(2):Article number 1340008Google Scholar
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    Chen N, Ghosh A (2010) Strongly stable assignment. In: Proceedings of the 18th annual European Symposium on Algorithms (ESA’10), Liverpool, UK. Lecture Notes in Computer Science, vol 6347. Springer, pp 147–158Google Scholar
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    Gale D, Shapley LS (1962) College admissions and the stability of marriage. Am Math Mon 69:9–15MathSciNetzbMATHCrossRefGoogle Scholar
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    Gusfield D, Irving RW (1989) The Stable Marriage Problem: Structure and Algorithms. MIT Press, Cambridge, USAzbMATHGoogle Scholar
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    http://www.nrmp.org (National Resident Matching Program website)
  9. 9.
    http://www.carms.ca (Canadian Resident Matching Service website)
  10. 10.
    http://www.jrmp.jp (Japan Resident Matching Program website)
  11. 11.
    Irving RW, Manlove DF, Scott S (2000) The Hospitals/Residents problem with Ties. In: Proceedings of the 7th Scandinavian Workshop on Algorithm Theory (SWAT’00), Bergen, Norway. Lecture Notes in Computer Science, vol 1851. Springer, pp 259–271Google Scholar
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    Irving RW, Manlove DF, Scott S (2002) Strong stability in the Hospitals/Residents problem. Technical report TR-2002-123, Department of Computing Science, University of Glasgow. Revised May 2005Google Scholar
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    Irving RW, Manlove DF, Sott S (2003) Strong stability in the Hospitals/Residents problem. In: Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science (STACS’03), Berlin, Germany. Lecture Notes in Computer Science, vol 2607. Springer, pp 439–450. Full version available as [12]Google Scholar
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    Kavitha T, Mehlhorn K, Michail D, Paluch KE (2007) Strongly stable matchings in time O(n m) and extension to the Hospitals-Residents problem. ACM Trans Algorithms 3(2):Article number 15Google Scholar
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    Manlove DF (2013) Algorithmics of matching under preferences. World Scientific, Hackensack, SingaporezbMATHCrossRefGoogle Scholar
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    Roth AE, Sotomayor MAO (1990) Two-sided matching: a study in game-theoretic modeling and analysis. Econometric society monographs, vol 18. Cambridge University Press, Cambridge/New York, USAGoogle Scholar
  19. 19.
    Scott S (2005) A study of stable marriage problems with ties. PhD thesis, Department of Computing Science, University of GlasgowGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.School of Computing Science, University of GlasgowGlasgowUK