Skip to main content
SpringerLink
Log in

A Constraint Programming Approach to the Hospitals / Residents Problem

  • Conference paper
Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4510))

Abstract

An instance I of the Hospitals / Residents problem (HR) involves a set of residents (graduating medical students) and a set of hospitals, where each hospital has a given capacity. The residents have preferences for the hospitals, as do hospitals for residents. A solution of I is a stable matching, which is an assignment of residents to hospitals that respects the capacity conditions and preference lists in a precise way. In this paper we present constraint encodings for HR that give rise to important structural properties. We also present a computational study using both randomly-generated and real-world instances. We provide additional motivation for our models by indicating how side constraints can be added easily in order to solve hard variants of HR.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aldershof, B., Carducci, O.M., Lorenc, D.C.: Refined inequalities for stable marriage. Constraints 4, 281–292 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bessière, C., Régin, J.-C.: Arc consistency for general constraint networks: Preliminary results. In: Proceedings of IJCAI ’97, vol. 1, pp. 398–404 (1997)

    Google Scholar 

  3. Brito, I., Meseguer, P.: Distributed stable matching problems. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 152–166. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  4. Brito, I., Meseguer, P.: Distributed stable matching problems with ties and incomplete lists. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 675–679. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  5. Canadian Resident Matching Service. How the matching algorithm works. Web document available at http://www.carms.ca/matching/algorith.htm

  6. Dias, V.M.F., da Fonseca, G.D., de Figueiredo, C.M.H., Szwarcfiter, J.L.: The stable marriage problem with restricted pairs. Theoretical Computer Science 306(1-3), 391–405 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gale, D., Shapley, L.S.: College admissions and the stability of marriage. American Mathematical Monthly 69, 9–15 (1962)

    Article  MATH  MathSciNet  Google Scholar 

  8. Gent, I.P., Irving, R.W., Manlove, D.F., Prosser, P., Smith, B.M.: A constraint programming approach to the stable marriage problem. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 225–239. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  9. Gent, I.P., Prosser, P.: An empirical study of the stable marriage problem with ties and incomplete lists. In: Proceedings of ECAI ’02, pp. 141–145. IOS Press, Amsterdam (2002)

    Google Scholar 

  10. Gent, I.P., Prosser, P.: SAT encodings of the stable marriage problem with ties and incomplete lists. In: Proceedings of SAT ’02, pp. 133–140 (2002)

    Google Scholar 

  11. Green, M.J., Cohen, D.A.: Tractability by approximating constraint languages. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 392–406. Springer, Heidelberg (2003)

    Google Scholar 

  12. Gusfield, D., Irving, R.W.: The Stable Marriage Problem: Structure and Algorithms. MIT Press, Cambridge (1989)

    MATH  Google Scholar 

  13. Irving, R.W.: Matching medical students to pairs of hospitals: a new variation on a well-known theme. In: Bilardi, G., Pietracaprina, A., Italiano, G.F., Pucci, G. (eds.) ESA 1998. LNCS, vol. 1461, pp. 381–392. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  14. Irving, R.W.: The Man-Exchange Stable Marriage Problem. Technical Report TR-2004-177, University of Glasgow, Department of Computing Science (2004)

    Google Scholar 

  15. Knuth, D.E.: Mariages Stables. Les Presses de L’Université de Montréal, Montréal (1976)

    MATH  Google Scholar 

  16. Lustig, I.J., Puget, J.: Program does not equal program: constraint programming and its relationship to mathematical programming. Interfaces 31, 29–53 (2001)

    Google Scholar 

  17. Mackworth, A.K.: Consistency in networks of relations. Artificial Intelligence 8, 99–118 (1977)

    Article  MATH  Google Scholar 

  18. Manlove, D.F., Irving, R.W., Iwama, K., Miyazaki, S., Morita, Y.: Hard variants of stable marriage. Theoretical Computer Science 276(1-2), 261–279 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  19. Manlove, D.F., O’Malley, G.: Modelling and solving the stable marriage problem using constraint programming. In: Proceedings of the Fifth Workshop on Modelling and Solving Problems with Constraints, held at IJCAI ’05, pp. 10–17 (2005)

    Google Scholar 

  20. Manlove, D.F., O’Malley, G., Prosser, P., Unsworth, C.: A Constraint Programming Approach to the Hospitals / Residents Problem. Technical Report TR-2007-236, University of Glasgow, Department of Computing Science (2007)

    Google Scholar 

  21. McDermid, E., Cheng, C., Suzuki, I.: Hardness results on the man-exchange stable marriage problem with short preference lists. Information Processing Letters 101, 13–19 (2007)

    Article  MathSciNet  Google Scholar 

  22. Ng, C., Hirschberg, D.S.: Lower bounds for the stable marriage problem and its variants. SIAM Journal on Computing 19, 71–77 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  23. National Resident Matching Program. About the NRMP. Web document available at http://www.nrmp.org/about_nrmp/how.html

  24. Ronn, E.: NP-complete stable matching problems. Journal of Algorithms 11, 285–304 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  25. Roth, A.E.: The evolution of the labor market for medical interns and residents: a case study in game theory. Journal of Political Economy 92(6), 991–1016 (1984)

    Article  Google Scholar 

  26. Roth, A.E., Sotomayor, M.A.O.: Two-sided matching: a study in game-theoretic modeling and analysis. Cambridge University Press, Cambridge (1990)

    MATH  Google Scholar 

  27. Silaghi, M.-C., Zanker, M., Barták, R.: Desk-mates (stable matching) with privacy of preferences, and a new distributed CSP framework. In: Proceedings of the CP 2004 workshop on CSP Techniques with Immediate Application (CSPIA), pp. 83–96 (2004)

    Google Scholar 

  28. Silaghi, M.-C., Abhyankar, A., Zanker, M., Barták, R.: Desk-mates (stable matching) with privacy of preferences, and a new distributed CSP framework. In: Proceedings of FLAIRS 2005, pp. 671–677. AAAI Press, Menlo Park (2005)

    Google Scholar 

  29. Unsworth, C., Prosser, P.: An n-ary constraint for the stable marriage problem. In: Proceedings of the Fifth Workshop on Modelling and Solving Problems with Constraints, held at IJCAI ’05, pp. 32–38 (2005)

    Google Scholar 

  30. Unsworth, C., Prosser, P.: A specialised binary constraint for the stable marriage problem. In: Zucker, J.-D., Saitta, L. (eds.) SARA 2005. LNCS (LNAI), vol. 3607, pp. 218–233. Springer, Heidelberg (2005)

    Google Scholar 

  31. van Hentenryck, P., Deville, Y., Teng, C.-M.: A generic arc-consistency algorithm and its specializations. Artificial Intelligence 57, 291–321 (1992)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK

    David F. Manlove, Gregg O’Malley, Patrick Prosser & Chris Unsworth

Authors
  1. David F. Manlove
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gregg O’Malley
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Patrick Prosser
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chris Unsworth
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Pascal Van Hentenryck Laurence Wolsey

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer Berlin Heidelberg

About this paper

Cite this paper

Manlove, D.F., O’Malley, G., Prosser, P., Unsworth, C. (2007). A Constraint Programming Approach to the Hospitals / Residents Problem. In: Van Hentenryck, P., Wolsey, L. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2007. Lecture Notes in Computer Science, vol 4510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72397-4_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-72397-4_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72396-7

  • Online ISBN: 978-3-540-72397-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation