Deligkas, A, Eiben, E, Ganian, R et al. (2 more authors) (Accepted: 2022) The Complexity of Envy-Free Graph Cutting. In: Proceedings of the 31st International Joint Conference on Artificial Intelligence. The 31st International Joint Conference on Artificial Intelligence, 23-29 Jul 2022, Vienna, Austria. International Joint Conferences on Artificial Intelligence , pp. 237-243. ISBN 978-0-9992411-9-6
Abstract
We consider the problem of fairly dividing a set of heterogeneous divisible resources among agents with different preferences. We focus on the setting where the resources correspond to the edges of a connected graph, every agent must be assigned a connected piece of this graph, and the fairness notion considered is the classical envy freeness. The problem is NP-complete, and we analyze its complexity with respect to two natural complexity measures: the number of agents and the number of edges in the graph. While the problem remains NP-hard even for instances with 2 agents, we provide a dichotomy characterizing the complexity of the problem when the number of agents is constant based on structural properties of the graph. For the latter case, we design a polynomial-time algorithm when the graph has a constant number of edges.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is an author produced version of a conference paper published in the Proceedings of the 31st International Joint Conference on Artificial Intelligence. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Agent-based and Multi-agent Systems: Resource Allocation; Agent-based and Multi-agent Systems: Computational Social Choice |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/V00252X/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 20 May 2022 13:33 |
Last Modified: | 24 Oct 2023 16:56 |
Published Version: | https://www.ijcai.org/proceedings/2022/34 |
Status: | Published |
Publisher: | International Joint Conferences on Artificial Intelligence |
Identification Number: | 10.24963/ijcai.2022/34 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:187107 |