{"type":"ScholarlyArticle","title":"Graphical Cake Cutting via Maximin Share","authors":[{"name":"Edith Elkind","slug":"edith-elkind","given":"Edith","family":"Elkind","affiliation":""},{"name":"Erel Segal-Halevi","slug":"erel-segal-halevi","given":"Erel","family":"Segal-Halevi","affiliation":""},{"name":"Warut Suksompong","slug":"warut-suksompong","given":"Warut","family":"Suksompong","affiliation":""}],"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.","doi":"10.24963/ijcai.2021/23","url":"https://ijcai.org/proceedings/2021/23","pdf":"https://ijcai.org/proceedings/2021/0023.pdf","markdown":"https://ijcai.org/proceedings/2021/23.md","bibtex":"https://ijcai.org/proceedings/2021/bibtex/23","volume":{"slug":"2021","title":"Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2021","url":"https://ijcai.org/proceedings/2021/","year":2021,"location":"Montreal","dates":"19-27 August 2021","editors":"Prof. Zhi-Hua Zhou","isbn":"978-0-9992411-9-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2021"},"section":"Agent-based and Multi-agent Systems","track":"Main Track","number":23,"pages":{"first":161,"last":167},"keywords":["Agent-based and Multi-agent Systems: Computational Social Choice","Agent-based and Multi-agent Systems: Resource Allocation"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}