{"type":"ScholarlyArticle","title":"Fair Division of a Graph into Compact Bundles","authors":[{"name":"Jayakrishnan Madathil","slug":"jayakrishnan-madathil","given":"Jayakrishnan","family":"Madathil","affiliation":"University of Glasgow , UK"}],"abstract":"We study the computational complexity of fair division of indivisible items in an enriched model: there is an underlying graph on the set of items. And we have to allocate the items (i.e., the vertices of the graph) to a set of agents in such a way that (a) the allocation is fair (for appropriate notions of fairness) and (b) each agent receives a bundle of items (i.e., a subset of vertices) that induces a subgraph with a specific ``nice structure.'' This model has previously been studied in the literature with the nice structure being a connected subgraph. In this paper, we propose an alternative for connectivity in fair division. We introduce compact graphs, and look for fair allocations in which each agent receives a compact bundle of items. Through compactness, we attempt to capture the idea that every agent must receive a bundle of ``closely related'' items. We prove a host of hardness and tractability results with respect to fairness concepts such as proportionality, envy-freeness and maximin share guarantee.","doi":"10.24963/ijcai.2023/316","url":"https://ijcai.org/proceedings/2023/316","pdf":"https://ijcai.org/proceedings/2023/0316.pdf","markdown":"https://ijcai.org/proceedings/2023/316.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/316","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":316,"pages":{"first":2835,"last":2843},"keywords":["Agent-based and Multi-agent Systems: MAS: Resource allocation","Game Theory and Economic Paradigms: GTEP: Fair division"],"videos":[],"references":[{"position":1,"raw":"[Amanatidis et al., 2022] Georgios Amanatidis, Geor- gios Birmpas, Aris Filos-Ratsikas, and Alexandros A. 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