Stable Assignment with Couples: Parameterized Complexity and Local Search

  • Dániel Marx
  • Ildikó Schlotter
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5917)


We study the Hospitals/Residents with Couples problem, a variant of the classical Stable Marriage problem. This is the extension of the Hospitals/Residents problem where residents are allowed to form pairs and submit joint rankings over hospitals. We use the framework of parameterized complexity, considering the number of couples as a parameter. We also apply a local search approach, and examine the possibilities for giving FPT algorithms applicable in this context. Furthermore, we also investigate the matching problem containing couples that is the simplified version of the Hospitals/Residents problem modeling the case when no preferences are given.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aarts, E.H.L., Lenstra, J.K. (eds.): Local Search in Combinatorial Optimization. Wiley, New York (1997)MATHGoogle Scholar
  2. 2.
    Alon, N., Yuster, R., Zwick, U.: Color-coding. J. ACM 42, 844–856 (1995)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Biró, P., McDermid, E.J.: Matching with couples is hard, but extra beds help (manuscript) (2009)Google Scholar
  4. 4.
    Fellows, M.R., Fomin, F.V., Lokshtanov, D., Rosamond, F.A., Saurabh, S., Villanger, Y.: Local search: Is brute-force avoidable? In: IJCAI 2009 (2009)Google Scholar
  5. 5.
    Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)Google Scholar
  6. 6.
    Gale, D., Shapley, L.S.: College admissions and the stability of marriage. American Mathematical Monthly 69, 9–15 (1962)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Gale, D., Sotomayor, M.: Some remarks on the stable matching problem. Discrete Appl. Math. 11, 223–232 (1985)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Glass, C.A., Kellerer, H.: Parallel machine scheduling with job assignment restrictions. Naval Research Logistics 54(3), 250–257 (2007)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Krokhin, A., Marx, D.: On the hardness of losing weight. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 662–673. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Klaus, B., Klijn, F.: Stable matchings and preferences of couples. J. Econ. Theory 121, 75–106 (2005)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Marx, D.: A parameterized view on matroid optimization problems. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 656–667. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Marx, D.: Local Search. Parameterized Complexity News 3, 7–8 (2008)Google Scholar
  13. 13.
    Marx, D.: Searching the k-change neighborhood for TSP is W[1]-hard. Oper. Res. Lett. 36(1), 31–36 (2008)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    McDermid, E.J., Manlove, D.F.: Keeping partners together: Algorithmic results for the Hospitals/Residents problem with couples. To appear in J. of Comb. Opt.Google Scholar
  15. 15.
    Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, Oxford (2006)MATHCrossRefGoogle Scholar
  16. 16.
    Ronn, E.: NP-Complete stable matching problems. J. Algorithms 11, 285–304 (1990)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Roth, A.E.: The evolution of the labor market for medical interns and residents: a case study in game theory. J. Polit. Econ. 92, 991–1016 (1984)CrossRefGoogle Scholar
  18. 18.
    Roth, A.E., Sotomayor, M.: Two Sided Matching: A Study in Game-Theoretic Modelling and Analysis. Cambridge University Press, Cambridge (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Dániel Marx
    • 1
  • Ildikó Schlotter
    • 1
  1. 1.Department of Computer Science and Information TheoryBudapest University of Technology and EconomicsBudapestHungary

Personalised recommendations