Graphical Cake Cutting via Maximin Share

Edith Elkind, Erel Segal-Halevi, Warut Suksompong

IJCAI 2021 pp. 161-167

doi:10.24963/IJCAI.2021/23 /ijcai/2021/elkind2021ijcai-graphical/

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.

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Cite

Text

Elkind et al. "Graphical Cake Cutting via Maximin Share." International Joint Conference on Artificial Intelligence, 2021. doi:10.24963/IJCAI.2021/23

Markdown

[Elkind et al. "Graphical Cake Cutting via Maximin Share." International Joint Conference on Artificial Intelligence, 2021.](https://mlanthology.org/ijcai/2021/elkind2021ijcai-graphical/) doi:10.24963/IJCAI.2021/23

BibTeX

@inproceedings{elkind2021ijcai-graphical,
  title     = {{Graphical Cake Cutting via Maximin Share}},
  author    = {Elkind, Edith and Segal-Halevi, Erel and Suksompong, Warut},
  booktitle = {International Joint Conference on Artificial Intelligence},
  year      = {2021},
  pages     = {161-167},
  doi       = {10.24963/IJCAI.2021/23},
  url       = {https://mlanthology.org/ijcai/2021/elkind2021ijcai-graphical/}
}