"Almost-stable" matchings in the Hospitals / Residents problem with Couples

Manlove, D. F. , McBride, I. and Trimble, J. (2017) "Almost-stable" matchings in the Hospitals / Residents problem with Couples. Constraints, 22(1), pp. 50-72. (doi: 10.1007/s10601-016-9249-7)

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The Hospitals / Residents problem with Couples (hrc) models the allocation of intending junior doctors to hospitals where couples are allowed to submit joint preference lists over pairs of (typically geographically close) hospitals. It is known that a stable matching need not exist, so we consider min bp hrc, the problem of finding a matching that admits the minimum number of blocking pairs (i.e., is “as stable as possible”). We show that this problem is NP-hard and difficult to approximate even in the highly restricted case that each couple finds only one hospital pair acceptable. However if we further assume that the preference list of each single resident and hospital is of length at most 2, we give a polynomial-time algorithm for this case. We then present the first Integer Programming (IP) and Constraint Programming (CP) models for min bp hrc. Finally, we discuss an empirical evaluation of these models applied to randomly-generated instances of min bp hrc. We find that on average, the CP model is about 1.15 times faster than the IP model, and when presolving is applied to the CP model, it is on average 8.14 times faster. We further observe that the number of blocking pairs admitted by a solution is very small, i.e., usually at most 1, and never more than 2, for the (28,000) instances considered.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Manlove, Professor David and Trimble, Mr James
Authors: Manlove, D. F., McBride, I., and Trimble, J.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Constraints
Publisher:Springer Verlag
ISSN (Online):1572-9354
Published Online:11 August 2016
Copyright Holders:Copyright © 2016 The Authors
First Published:First published in Constraints 22(1): 50-72
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
607071Efficient Algorithms for Mechanism Design Without Monetary Transfer.David ManloveEngineering & Physical Sciences Research Council (EPSRC)EP/K010042/1COM - COMPUTING SCIENCE
709601EPSRC: ISF 2015 - Runtime Verification of Autonomous AgentsAlice MillerEngineering & Physical Sciences Research Council (EPSRC)EP/N508792/1COM - COMPUTING SCIENCE