Graphical Cake Cutting via Maximin Share

Edith Elkind; Erel Segal-Halevi; Warut Suksompong

doi:10.24963/ijcai.2021/23

Graphical Cake Cutting via Maximin Share

Edith Elkind, Erel Segal-Halevi, Warut Suksompong

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

12 Scopus citations

Abstract

We study the recently introduced cake-cutting setting in which the cake is represented by an undirected graph. This generalizes the canonical interval cake and allows for modeling the division of road networks. We show that when the graph is a forest, an allocation satisfying the well-known criterion of maximin share fairness always exists. Our result holds even when separation constraints are imposed; however, in the latter case no multiplicative approximation of proportionality can be guaranteed. Furthermore, while maximin share fairness is not always achievable for general graphs, we prove that ordinal relaxations can be attained.

Original language	English
Title of host publication	Proceedings of the 30th International Joint Conference on Artificial Intelligence, IJCAI 2021
Editors	Zhi-Hua Zhou
Publisher	International Joint Conferences on Artificial Intelligence
Pages	161-167
Number of pages	7
ISBN (Electronic)	9780999241196
DOIs	https://doi.org/10.24963/ijcai.2021/23
State	Published - 2021
Externally published	Yes
Event	30th International Joint Conference on Artificial Intelligence, IJCAI 2021 - Virtual, Online, Canada Duration: 19 Aug 2021 → 27 Aug 2021

Publication series

Name	IJCAI International Joint Conference on Artificial Intelligence
ISSN (Print)	1045-0823

Conference

Conference	30th International Joint Conference on Artificial Intelligence, IJCAI 2021
Country/Territory	Canada
City	Virtual, Online
Period	19/08/21 → 27/08/21

Bibliographical note

Publisher Copyright:
© 2021 International Joint Conferences on Artificial Intelligence. All rights reserved.

Funding

This work was partially supported by the Israel Science Foundation under grant number 712/20 and by an NUS Start-up Grant. We would like to thank the anonymous reviewers for their valuable comments.

Funders	Funder number
Horizon 2020 Framework Programme	639945
National University of Singapore
Israel Science Foundation	712/20

Access to Document

10.24963/ijcai.2021/23

Cite this

Elkind, E., Segal-Halevi, E., & Suksompong, W. (2021). Graphical Cake Cutting via Maximin Share. In Z.-H. Zhou (Ed.), Proceedings of the 30th International Joint Conference on Artificial Intelligence, IJCAI 2021 (pp. 161-167). (IJCAI International Joint Conference on Artificial Intelligence). International Joint Conferences on Artificial Intelligence. https://doi.org/10.24963/ijcai.2021/23

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abstract = "We study the recently introduced cake-cutting setting in which the cake is represented by an undirected graph. This generalizes the canonical interval cake and allows for modeling the division of road networks. We show that when the graph is a forest, an allocation satisfying the well-known criterion of maximin share fairness always exists. Our result holds even when separation constraints are imposed; however, in the latter case no multiplicative approximation of proportionality can be guaranteed. Furthermore, while maximin share fairness is not always achievable for general graphs, we prove that ordinal relaxations can be attained.",

author = "Edith Elkind and Erel Segal-Halevi and Warut Suksompong",

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doi = "10.24963/ijcai.2021/23",

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Elkind, E, Segal-Halevi, E & Suksompong, W 2021, Graphical Cake Cutting via Maximin Share. in Z-H Zhou (ed.), Proceedings of the 30th International Joint Conference on Artificial Intelligence, IJCAI 2021. IJCAI International Joint Conference on Artificial Intelligence, International Joint Conferences on Artificial Intelligence, pp. 161-167, 30th International Joint Conference on Artificial Intelligence, IJCAI 2021, Virtual, Online, Canada, 19/08/21. https://doi.org/10.24963/ijcai.2021/23

Graphical Cake Cutting via Maximin Share. / Elkind, Edith; Segal-Halevi, Erel; Suksompong, Warut.
Proceedings of the 30th International Joint Conference on Artificial Intelligence, IJCAI 2021. ed. / Zhi-Hua Zhou. International Joint Conferences on Artificial Intelligence, 2021. p. 161-167 (IJCAI International Joint Conference on Artificial Intelligence).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Graphical Cake Cutting via Maximin Share

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