Algorithms for New Types of Fair Stable Matchings

Cooper, F. and Manlove, D. (2020) Algorithms for New Types of Fair Stable Matchings. In: 18th International Symposium on Experimental Algorithms (SEA 2020), Catania, Italy, 16-18 Jun 2020, p. 20. ISBN 9783959771481 (doi:10.4230/LIPIcs.SEA.2020.20)

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Abstract

We study the problem of finding "fair" stable matchings in the Stable Marriage problem with Incomplete lists (SMI). For an instance I of SMI there may be many stable matchings, providing significantly different outcomes for the sets of men and women. We introduce two new notions of fairness in SMI. Firstly, a regret-equal stable matching minimises the difference in ranks of a worst-off man and a worst-off woman, among all stable matchings. Secondly, a min-regret sum stable matching minimises the sum of ranks of a worst-off man and a worst-off woman, among all stable matchings. We present two new efficient algorithms to find stable matchings of these types. Firstly, the Regret-Equal Degree Iteration Algorithm finds a regret-equal stable matching in O(d0nm) time, where d0 is the absolute difference in ranks between a worst-off man and a worst-off woman in the man-optimal stable matching, n is the number of men or women, and m is the total length of all preference lists. Secondly, the Min-Regret Sum Algorithm finds a min-regret sum stable matching in O(dsm) time, where ds is the difference in the ranks between a worst-off man in each of the woman-optimal and man-optimal stable matchings. Experiments to compare several types of fair optimal stable matchings were conducted and show that the Regret-Equal Degree Iteration Algorithm produces matchings that are competitive with respect to other fairness objectives. On the other hand, existing types of "fair" stable matchings did not provide as close an approximation to regret-equal stable matchings.

Item Type:Conference Proceedings
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Manlove, Professor David and Cooper, Frances
Authors: Cooper, F., and Manlove, D.
College/School:College of Science and Engineering > School of Computing Science
ISSN:1868-8969
ISBN:9783959771481
Copyright Holders:Copyright © 2020 The Authors
First Published:First published in 18th International Symposium on Experimental Algorithms (SEA 2020): 20
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
172865EPSRC DTP 16/17 and 17/18Tania GalabovaEngineering and Physical Sciences Research Council (EPSRC)EP/N509668/1Research and Innovation Services