Graphical Cake Cutting via Maximin Share

Edith Elkind; Erel Segal-Halevi; Warut Suksompong

IJCAI 2021poster16 citations

Graphical Cake Cutting via Maximin Share

Edith Elkind, Erel Segal-Halevi, Warut Suksompong

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.

Agent-based and Multi-agent Systems: Resource AllocationAgent-based and Multi-agent Systems: Computational Social Choice

BibTeX

@inproceedings{ijcai2021p23,
  title     = {Graphical Cake Cutting via Maximin Share},
  author    = {Elkind, Edith and Segal-Halevi, Erel and Suksompong, Warut},
  booktitle = {Proceedings of the Thirtieth International Joint Conference on
               Artificial Intelligence, {IJCAI-21}},
  publisher = {International Joint Conferences on Artificial Intelligence Organization},
  editor    = {Zhi-Hua Zhou},
  pages     = {161--167},
  year      = {2021},
  month     = {8},
  note      = {Main Track},
  doi       = {10.24963/ijcai.2021/23},
  url       = {https://doi.org/10.24963/ijcai.2021/23},
}