Solving hard stable matching problems involving groups of similar agents

Meeks, K. and Rastegari, B. (2020) Solving hard stable matching problems involving groups of similar agents. Theoretical Computer Science, 844, pp. 171-194. (doi: 10.1016/j.tcs.2020.08.017)

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Many important stable matching problems are known to be NP-hard, even when strong restrictions are placed on the input. In this paper we seek to identify structural properties of instances of stable matching problems which will allow us to design efficient algorithms using elementary techniques. We focus on the setting in which all agents involved in some matching problem can be partitioned into k different types, where the type of an agent determines his or her preferences, and agents have preferences over types (which may be refined by more detailed preferences within a single type). This situation would arise in practice if agents form preferences solely based on some small collection of agents' attributes. We also consider a generalisation in which each agent may consider some small collection of other agents to be exceptional, and rank these in a way that is not consistent with their types; this could happen in practice if agents have prior contact with a small number of candidates. We show that (for the case without exceptions), several well-studied NP-hard stable matching problems including Max SMTI (that of finding the maximum cardinality stable matching in an instance of stable marriage with ties and incomplete lists) belong to the parameterised complexity class FPT when parameterised by the number of different types of agents needed to describe the instance. For Max SMTI this tractability result can be extended to the setting in which each agent promotes at most one “exceptional” candidate to the top of his/her list (when preferences within types are not refined), but the problem remains NP-hard if preference lists can contain two or more exceptions and the exceptional candidates can be placed anywhere in the preference lists, even if the number of types is bounded by a constant.

Item Type:Articles
Additional Information:The first author is supported by a Personal Research Fellowship from the Royal Society of Edinburgh (funded by the Scottish Government).
Glasgow Author(s) Enlighten ID:Rastegari, Dr Baharak and Meeks, Dr Kitty
Authors: Meeks, K., and Rastegari, B.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Theoretical Computer Science
ISSN (Online):1879-2294
Published Online:19 August 2020
Copyright Holders:Copyright © 2020 Elsevier
First Published:First published in Theoretical Computer Science 844: 171-194
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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