{"type":"ScholarlyArticle","title":"The Parameterized Complexity of Connected Fair Division","authors":[{"name":"Argyrios Deligkas","slug":"argyrios-deligkas","given":"Argyrios","family":"Deligkas","affiliation":""},{"name":"Eduard Eiben","slug":"eduard-eiben","given":"Eduard","family":"Eiben","affiliation":""},{"name":"Robert Ganian","slug":"robert-ganian","given":"Robert","family":"Ganian","affiliation":""},{"name":"Thekla Hamm","slug":"thekla-hamm","given":"Thekla","family":"Hamm","affiliation":""},{"name":"Sebastian Ordyniak","slug":"sebastian-ordyniak","given":"Sebastian","family":"Ordyniak","affiliation":""}],"abstract":"We study the Connected Fair Division problem (CFD), which generalizes the fundamental problem of fairly allocating resources to agents by requiring that the items allocated to each agent form a connected subgraph in a provided item graph G. We expand on previous results by providing a comprehensive complexity-theoretic understanding of CFD based on several new algorithms and lower bounds while taking into account several well-established notions of fairness: proportionality, envy-freeness, EF1 and EFX. In particular, we show that to achieve tractability, one needs to restrict both the agents and the item graph in a meaningful way. We design (XP)-algorithms for the problem parameterized by (1) clique-width of G plus the number of agents and (2) treewidth of G plus the number of agent types, along with corresponding lower bounds. Finally, we show that to achieve fixed-parameter tractability, one needs to not only use a more restrictive parameterization of G, but also include the maximum item valuation as an additional parameter.","doi":"10.24963/ijcai.2021/20","url":"https://ijcai.org/proceedings/2021/20","pdf":"https://ijcai.org/proceedings/2021/0020.pdf","markdown":"https://ijcai.org/proceedings/2021/20.md","bibtex":"https://ijcai.org/proceedings/2021/bibtex/20","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":20,"pages":{"first":139,"last":145},"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."}