{"type":"ScholarlyArticle","title":"Approximate Envy-Freeness in Graphical Cake Cutting","authors":[{"name":"Sheung Man Yuen","slug":"sheung-man-yuen","given":"Sheung Man","family":"Yuen","affiliation":"National University of Singapore"},{"name":"Warut Suksompong","slug":"warut-suksompong","given":"Warut","family":"Suksompong","affiliation":"National University of Singapore"}],"abstract":"We study the problem of fairly allocating a divisible resource in the form of a graph, also known as graphical cake cutting. Unlike for the canonical interval cake, a connected envy-free allocation is not guaranteed to exist for a graphical cake. We focus on the existence and computation of connected allocations with low envy. For general graphs, we show that there is always a 1/2-additive-envy-free allocation and, if the agents' valuations are identical, a (2+\\epsilon)-multiplicative-envy-free allocation for any \\epsilon > 0. In the case of star graphs, we obtain a multiplicative factor of 3+\\epsilon for arbitrary valuations and 2 for identical valuations. We also derive guarantees when each agent can receive more than one connected piece. All of our results come with efficient algorithms for computing the respective allocations.","doi":"10.24963/ijcai.2023/326","url":"https://ijcai.org/proceedings/2023/326","pdf":"https://ijcai.org/proceedings/2023/0326.pdf","markdown":"https://ijcai.org/proceedings/2023/326.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/326","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":326,"pages":{"first":2923,"last":2930},"keywords":["Game Theory and Economic Paradigms: GTEP: Fair division","Game Theory and Economic Paradigms: GTEP: Computational social choice"],"videos":[],"references":[{"position":1,"raw":"[Arunachaleswaran et al., 2019] Eshwar Ram Arunachaleswaran, Siddharth Barman, Rachitesh Kumar, and Nidhi Rathi. 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