{"type":"ScholarlyArticle","title":"Dividing Conflicting Items Fairly","authors":[{"name":"Ayumi Igarashi","slug":"ayumi-igarashi","given":"Ayumi","family":"Igarashi","affiliation":""},{"name":"Pasin Manurangsi","slug":"pasin-manurangsi","given":"Pasin","family":"Manurangsi","affiliation":""},{"name":"Hirotaka Yoneda","slug":"hirotaka-yoneda","given":"Hirotaka","family":"Yoneda","affiliation":""}],"abstract":"We study the allocation of indivisible goods under conflicting constraints, represented by a graph. In this framework, vertices correspond to goods and edges correspond to conflicts between a pair of goods. Each agent is allocated an independent set in the graph. In a recent work of Kumar et al. (AAMAS, 2024), it was shown that a maximal EF1 allocation exists for interval graphs and two agents with monotone valuations. We significantly extend this result by establishing that a maximal EF1 allocation exists for any graph when the two agents have monotone valuations. To compute such an allocation, we present a polynomial-time algorithm for additive valuations, as well as a pseudo-polynomial time algorithm for monotone valuations. Moreover, we complement our findings by providing a counterexample demonstrating a maximal EF1 allocation may not exist for three agents with monotone valuations; further, we establish NP-hardness of determining the existence of such allocations for every fixed number n >= 3 of agents. All of our results for goods also apply to the allocation of chores.","doi":"10.24963/ijcai.2025/435","url":"https://ijcai.org/proceedings/2025/435","pdf":"https://ijcai.org/proceedings/2025/0435.pdf","markdown":"https://ijcai.org/proceedings/2025/435.md","bibtex":"https://ijcai.org/proceedings/2025/bibtex/435","volume":{"slug":"2025","title":"Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2025","url":"https://ijcai.org/proceedings/2025/","year":2025,"location":"Montreal, Canada","dates":"16-22 August 2025","editors":"James Kwok","isbn":"978-1-956792-06-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2025"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":435,"pages":{"first":3908,"last":3915},"keywords":["Game Theory and Economic Paradigms: GTEP: Computational social choice","Game Theory and Economic Paradigms: GTEP: Fair division"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}