Stable Marriage with Groups of Similar Agents

Meeks, K. and Rastegari, B. (2018) Stable Marriage with Groups of Similar Agents. In: WINE 2018: The 14th Conference on Web and Internet Economics, Oxford, United Kingdom, 15-17 Dec 2018, pp. 312-326. ISBN 9783030046118 (doi:10.1007/978-3-030-04612-5_21)

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Abstract

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), the well-known NP-hard matching problem Max SMTI (that of finding the maximum cardinality stable matching in an instance of stable marriage with ties and incomplete lists) belongs to the parameterised complexity class FPT when parameterised by the number of different types of agents needed to describe the instance. 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.

Item Type:Conference Proceedings
Status:Published
Refereed:Yes
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
ISSN:0302-9743
ISBN:9783030046118
Copyright Holders:Copyright © 2018 Springer Nature Switzerland AG
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher
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