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 \(R =\{ r_{1},\ldots,r_{n}\}\) of residents and a set \(H =\{ h_{1},\ldots,h_{m}\}\) of hospitals. Each hospital h j ∈ H has a positive integral capacity, denoted by c j . Also, each resident r i ∈ R has a preference list in which he ranks in strict order a subset of H. A pair \((r_{i},h_{j}) \in R \times H\) is said to be acceptable if h j appears in r i ’s preference list; in this case r i is said to find h j acceptable. Similarly each hospital h j ∈ H has a preference list in which it ranks in strict order those residents who find h j acceptable. Given any three agents \(x,y,z \in R \cup H\), x is said to prefer y to z if x finds each of y and z acceptable, and y precedes z...
Recommended Reading
Abdulkadiroǧlu A, Pathak PA, Roth AE (2005) The New York city high school match. Am Econ Rev 95(2):364–367
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 85–96
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Gusfield D, Irving RW (1989) The Stable Marriage Problem: Structure and Algorithms. MIT Press, Cambridge, USA
http://www.nrmp.org (National Resident Matching Program website)
http://www.carms.ca (Canadian Resident Matching Service website)
http://www.jrmp.jp (Japan Resident Matching Program website)
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 259–271
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 2005
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]
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Manlove, D.F. (2015). The Hospitals/Residents Problem. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27848-8_180-2
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