The Three-Dimensional Stable Roommates Problem with Additively Separable Preferences

McKay, M. and Manlove, D. (2021) The Three-Dimensional Stable Roommates Problem with Additively Separable Preferences. In: 14th International Symposium on Algorithmic Game Theory (SAGT 2021), Aarhus, Denmark, 21-24 Sep 2021, pp. 266-280. ISBN 9783030859466 (doi: 10.1007/978-3-030-85947-3_18)

Abstract

The Stable Roommates problem involves matching a set of agents into pairs based on the agents’ strict ordinal preference lists. The matching must be stable, meaning that no two agents strictly prefer each other to their assigned partners. A number of three-dimensional variants exist, in which agents are instead matched into triples. Both the original problem and these variants can also be viewed as hedonic games. We formalise a three-dimensional variant using general additively separable preferences, in which each agent provides an integer valuation of every other agent. In this variant, we show that a stable matching may not exist and that the related decision problem is NP -complete, even when the valuations are binary. In contrast, we show that if the valuations are binary and symmetric then a stable matching must exist and can be found in polynomial time. We also consider the related problem of finding a stable matching with maximum utilitarian welfare when valuations are binary and symmetric. We show that this optimisation problem is NP -hard and present a novel 2-approximation algorithm.

• Item Type: Conference Proceedings
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: McKay, Mr Michael and Manlove, Professor David
• Authors: McKay, M., and Manlove, D.
• College/School: College of Science and Engineering > School of Computing Science
• ISSN: 0302-9743
• ISBN: 9783030859466
• Copyright Holders: Copyright © 2021 Springer Nature Switzerland AG
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher

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• Organisation

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
305200		DTP 2018-19 University of Glasgow	Mary Beth Kneafsey	Engineering and Physical Sciences Research Council (EPSRC)	EP/R513222/1	MVLS - Graduate School
300808		IP-MATCH: Integer Programming for Large and Complex Matching Problems	David Manlove	Engineering and Physical Sciences Research Council (EPSRC)	EP/P028306/1	Computing Science