Abstract
The Hospitals / Residents problem with Couples (hrc) is a generalisation of the classical Hospitals / Residents problem (hr) that is important in practical applications because it models the case where couples submit joint preference lists over pairs of (typically geographically close) hospitals. In this paper we give a new NP-completeness result for the problem of deciding whether a stable matching exists, in highly restricted instances of hrc, and also an inapproximability bound for finding a matching with the minimum number of blocking pairs in equally restricted instances of hrc. Further, we present a full description of the first Integer Programming model for finding a maximum cardinality stable matching in an instance of hrc and we describe empirical results when this model applied to randomly generated instances of hrc.
A preliminary version of this paper appeared in the Proceedings of OR 2013.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Abraham, D.J., Biró, P., Manlove, D.F.: “Almost stable” matchings in the roommates problem. In: Erlebach, T., Persinao, G. (eds.) WAOA 2005. LNCS, vol. 3879, pp. 1–14. Springer, Heidelberg (2006)
Aldershof, B., Carducci, O.M.: Stable matching with couples. Discrete Appl. Math. 68, 203–207 (1996)
Ashlagi, I., Braverman, M., Hassidim, A.: Matching with couples revisited. Tech. Rep. arXiv: 1011.2121, Cornell University Library (2010)
Berman, P., Karpinski, M., Scott, A.D.: Approximation hardness of short symmetric instances of MAX-3SAT. Tech. Rep. 49, ECCC (2003)
Biró, P.: Student admissions in Hungary as Gale and Shapley envisaged. Tech. Rep. TR-2008-291, University of Glasgow, Dept. of Computing Science (2008)
Biró, P., Irving, R.W., Schlotter, I.: Stable matching with couples: an empirical study. ACM J. Exp. Algorithmics 16, section 1, article 2 (2011)
Biró, P., Klijn, F.: Matching with couples: a multidisciplinary survey. International Game Theory Review 15(2), article number 1340008 (2013)
Biró, P., Manlove, D.F., McBride, I.: The hospitals / residents problem with couples: Complexity and integer programming models. Tech. Rep. arXiv: 1308.4534, Cornell University Library (2013)
Canadian Resident Matching Service, http://www.carms.ca
Gale, D., Shapley, L.S.: College admissions and the stability of marriage. Amer. Math. Monthly 69, 9–15 (1962)
Gale, D., Sotomayor, M.: Some remarks on the stable matching problem. Discrete Appl. Math. 11, 223–232 (1985)
Gusfield, D., Irving, R.W.: The Stable Marriage Problem: Structure and Algorithms. MIT Press, Boston (1989)
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)
Japan Resident Matching Program, http://www.jrmp.jp
Manlove, D.F.: Algorithmics of Matching Under Preferences. World Scientific, Singapore (2013)
McDermid, E.J., Manlove, D.F.: Keeping partners together: Algorithmic results for the hospitals / residents problem with couples. J. Comb. Optim. 19(3), 279–303 (2010)
Ng, C., Hirschberg, D.S.: Lower bounds for the stable marriage problem and its variants. SIAM J. Comput. 19, 71–77 (1990)
National Resident Matching Program, http://www.nrmp.org
Ronn, E.: NP-complete stable matching problems. J. Algorithms 11, 285–304 (1990)
Roth, A.E.: The evolution of the labor market for medical interns and residents: A case study in game theory. J. Political Economy 92(6), 991–1016 (1984)
Roth, A.E.: On the allocation of residents to rural hospitals: A general property of two-sided matching markets. Econometrica 54, 425–427 (1986)
Roth, A.E., Peranson, E.: The effects of the change in the NRMP matching algorithm. J. Amer. Medical Assoc. 278(9), 729–732 (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Biró, P., Manlove, D.F., McBride, I. (2014). The Hospitals / Residents Problem with Couples: Complexity and Integer Programming Models. In: Gudmundsson, J., Katajainen, J. (eds) Experimental Algorithms. SEA 2014. Lecture Notes in Computer Science, vol 8504. Springer, Cham. https://doi.org/10.1007/978-3-319-07959-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-07959-2_2
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07958-5
Online ISBN: 978-3-319-07959-2
eBook Packages: Computer ScienceComputer Science (R0)