Improving solution times for stable matching problems through preprocessing

William Petterssona, Maxence Delorme, Sergio Garcia, Jacek Gondzio, Jӧrg Kalcsics, David Manlove

Research output: Contribution to journalArticlepeer-review

Abstract

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 showthat, when solving MAX-HRT instances with ties on both sides, our new techniques can reduce runtimes
by up to 55%.
Original languageEnglish
Number of pages39
JournalComputers and Operations Research
Early online date26 Oct 2020
DOIs
Publication statusE-pub ahead of print - 26 Oct 2020

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