Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Hospitals/Residents Problems with Quota Lower Bounds

  • Huang Chien-ChungEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_675

Years and Authors of Summarized Original Work

  • 2010; Biró, Fleiner, Irving, Manlove;

  • 2010; Huang;

  • 2011; Hamada, Iwama, Miyazaki;

  • 2012; Fleiner, Kamiyama

Problem Definition

The Hospitals/Residents (HR) problem is the many-to-one version of the stable marriage problem introduced by Gale and Shapley. In this problem, a bipartite graph \(G = (\mathcal{R}\cup \mathcal{H},E)\)


Hospitals/Residents problem Lower quotas Stable matching 
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Recommended Reading

  1. 1.
    Biro P, Fleiner T, Irving RW, Manlove DF (2010) The College Admissions problem with lower and common quotas. Theor Comput Sci 411(34–36):3136–3153MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Fleiner T, Kamiyama N (2012) A matroid approach to stable matchings with lower quotas In: 23nd annual ACM-SIAM symposium on discrete algorithms, Kyoto, pp 135–142Google Scholar
  3. 3.
    Hamada K, Iwama K, Miyazaki S (2011) The Hospitals/Residents problem with quota lower bounds. In: 19th annual European symposium on algorithms, Saarbrücken, vol 411(34–36), pp 180–191MathSciNetzbMATHGoogle Scholar
  4. 4.
    Huang C-C (2010) Classified stable matching. In: 21st annual ACM-SIAM symposium on discrete algorithms, Austin, pp 1235–1253Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Chalmers University of Technology and University of GothenburgGothenburgSweden