{"type":"ScholarlyArticle","title":"Complexity Results and Exact Algorithms for Fair Division of Indivisible Items: A Survey","authors":[{"name":"Trung Thanh Nguyen","slug":"trung-thanh-nguyen","given":"Trung Thanh","family":"Nguyen","affiliation":"ORLab , Faculty of Computer Science , Phenikaa University , 12116 Hanoi , Vietnam"},{"name":"Jörg Rothe","slug":"jorg-rothe","given":"Jörg","family":"Rothe","affiliation":"Institut für Informatik , Heinrich-Heine-Universität Düsseldorf , 40225 Düsseldorf , Germany"}],"abstract":"Fair allocation of indivisible goods is a central topic in many AI applications. Unfortunately, the corresponding problems are known to be NP-hard for many fairness concepts, so unless P = NP, exact polynomial-time algorithms cannot exist for them. In practical applications, however, it would be highly desirable to find exact solutions as quickly as possible. This motivates the study of algorithms that—even though they only run in exponential time—are as fast as possible and exactly solve such problems. We present known complexity results for them and give a survey of important techniques for designing such algorithms, mainly focusing on four common fairness notions: max-min fairness, maximin share, maximizing Nash social welfare, and envy-freeness. We also highlight the most challenging open problems for future work.","doi":"10.24963/ijcai.2023/754","url":"https://ijcai.org/proceedings/2023/754","pdf":"https://ijcai.org/proceedings/2023/0754.pdf","markdown":"https://ijcai.org/proceedings/2023/754.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/754","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":"Survey Track","track":"Survey Track","number":754,"pages":{"first":6732,"last":6740},"keywords":["Survey: Game Theory and Economic Paradigms","Survey: Agent-based and Multi-agent Systems","Survey: AI Ethics, Trust, Fairness"],"videos":[],"references":[{"position":1,"raw":"[Akrami et al., 2022] Hannaneh Akrami, Bhaskar Ray Chaudhury, Martin Hoefer, Kurt Mehlhorn, Marco Schmalhofer, Golnoosh Shahkarami, Giovanna Var- ricchio, Quentin Vermande, and Ernest van Wijland. 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