{"type":"ScholarlyArticle","title":"Fair Division of a Graph","authors":[{"name":"Sylvain Bouveret","slug":"sylvain-bouveret","given":"Sylvain","family":"Bouveret","affiliation":"LIG -Grenoble INP , France"},{"name":"Katarína Cechlárová","slug":"katarina-cechlarova","given":"Katarína","family":"Cechlárová","affiliation":"P.J. Šafárik University , Slovakia"},{"name":"Edith Elkind","slug":"edith-elkind","given":"Edith","family":"Elkind","affiliation":"University of Oxford , UK"},{"name":"Ayumi Igarashi","slug":"ayumi-igarashi","given":"Ayumi","family":"Igarashi","affiliation":"University of Oxford , UK"},{"name":"Dominik Peters","slug":"dominik-peters","given":"Dominik","family":"Peters","affiliation":"University of Oxford , UK"}],"abstract":"We consider fair allocation of indivisible items under an additional constraint: there is an undirected graph describing the relationship between the items, and each agent's share must form a connected subgraph of this graph. This framework captures, e.g., fair allocation of land plots, where the graph describes the accessibility relation among the plots. We focus on agents that have additive utilities for the items, and consider several common fair division solution concepts, such as proportionality, envy-freeness and maximin share guarantee. While finding good allocations according to these solution concepts is computationally hard in general, we design efficient algorithms for special cases wherethe underlying graph has simple structure, and/or the number of agents---or, less restrictively, the number of agent types---is small. In particular, despite non-existence results in the general case, we prove that for acyclic graphs a maximin share allocation always exists and can be found efficiently.","doi":"10.24963/ijcai.2017/20","url":"https://ijcai.org/proceedings/2017/20","pdf":"https://ijcai.org/proceedings/2017/0020.pdf","markdown":"https://ijcai.org/proceedings/2017/20.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/20","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":20,"pages":{"first":135,"last":141},"keywords":["Agent-based and Multi-agent Systems: Social Choice Theory","Agent-based and Multi-agent Systems: Economic paradigms, auctions and market-based systems"],"videos":[],"references":[{"position":1,"raw":"[Abebe et al., 2017] R. 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