Improving solution times of stable matching problems through preprocessing

Pettersson, W. , Delorme, M., García, S., Gondzio, J., Kalcsics, J. and Manlove, D. (2021) Improving solution times of stable matching problems through preprocessing. Computers and Operations Research, 128, 105128. (doi: 10.1016/j.cor.2020.105128)

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We present new theory, heuristics, and algorithms for preprocessing instances of the Stable Marriage problem with Ties and Incomplete lists (SMTI) and the Hospitals/Residents problem with Ties (HRT). Instances of these problems can be preprocessed by removing from the preference lists of some agents entries such that the set of stable matchings is not affected. Removing such entries reduces the problem size, creating smaller models that can be more easily solved by integer programming (IP) solvers. The new theorems are the first to describe when preference list entries can be removed from instances of HRT when ties are present on both sides, and also extend existing results on preprocessing instances of SMTI. A number of heuristics, as well as an IP model and a graph-based algorithm, are presented to find and perform this preprocessing. Experimental results show that our new graph-based algorithm achieves a 44% reduction in the average running time to find a maximum weight stable matching in real-world instances of SMTI compared to existing preprocessing techniques, and 80% compared to not using preprocessing. We also show that, when solving MAX-HRT instances with ties on both sides, our new techniques can reduce runtimes by up to 55%.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Manlove, Professor David and Pettersson, Dr William
Authors: Pettersson, W., Delorme, M., García, S., Gondzio, J., Kalcsics, J., and Manlove, D.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Computers and Operations Research
ISSN (Online):1873-765X
Published Online:26 October 2020
Copyright Holders:Copyright © 2020 The Authors
First Published:First published in Computers and Operations Research 128: 105128
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
300808IP-MATCH: Integer Programming for Large and Complex Matching ProblemsDavid ManloveEngineering and Physical Sciences Research Council (EPSRC)EP/P028306/1Computing Science