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Stable marriage with groups of similar agents

Stable marriage with groups of similar agents
Stable marriage with groups of similar agents
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.
312-326
Springer
Meeks, Kitty
d068f6a9-2e17-4337-b1e8-d93141225713
Rastegari, Baharak
6ba9e93c-53ba-4090-8f77-c1cb1568d7d1
Meeks, Kitty
d068f6a9-2e17-4337-b1e8-d93141225713
Rastegari, Baharak
6ba9e93c-53ba-4090-8f77-c1cb1568d7d1

Meeks, Kitty and Rastegari, Baharak (2018) Stable marriage with groups of similar agents. In Web and Internet Economics: WINE 2018. vol. 11316, Springer. pp. 312-326 . (doi:10.1007/978-3-030-04612-5_21).

Record type: Conference or Workshop Item (Paper)

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.

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More information

Accepted/In Press date: 24 September 2018
e-pub ahead of print date: 21 November 2018
Venue - Dates: WINE 2018: The 14th Conference on Web and Internet Economics, , Oxford, United Kingdom, 2018-12-15 - 2018-12-17

Identifiers

Local EPrints ID: 425759
URI: http://eprints.soton.ac.uk/id/eprint/425759
PURE UUID: cbafe9fb-511d-467a-877b-6da28b31039c
ORCID for Baharak Rastegari: ORCID iD orcid.org/0000-0002-0985-573X

Catalogue record

Date deposited: 02 Nov 2018 17:30
Last modified: 10 Nov 2021 03:56

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Contributors

Author: Kitty Meeks
Author: Baharak Rastegari ORCID iD

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