{"type":"ScholarlyArticle","title":"Simplification and Improvement of MMS Approximation","authors":[{"name":"Hannaneh Akrami","slug":"hannaneh-akrami","given":"Hannaneh","family":"Akrami","affiliation":"Max Planck Institute for Informatics , Germany; Graduiertenschule Informatik , Universität des Saarlandes , Germany"},{"name":"Jugal Garg","slug":"jugal-garg","given":"Jugal","family":"Garg","affiliation":"University of Illinois at Urbana-Champaign , USA"},{"name":"Eklavya Sharma","slug":"eklavya-sharma","given":"Eklavya","family":"Sharma","affiliation":"University of Illinois at Urbana-Champaign , USA"},{"name":"Setareh Taki","slug":"setareh-taki","given":"Setareh","family":"Taki","affiliation":"Grubhub , USA"}],"abstract":"We consider the problem of fairly allocating a set of indivisible goods among n agents with additive valuations, using the popular fairness notion of maximin share (MMS). Since MMS allocations do not always exist, a series of works provided existence and algorithms for approximate MMS allocations. The Garg-Taki algorithm gives the current best approximation factor of (3/4 + 1/12n). Most of these results are based on complicated analyses, especially those providing better than 2/3 factor. Moreover, since no tight example is known of the Garg-Taki algorithm, it is unclear if this is the best factor of this approach. In this paper, we significantly simplify the analysis of this algorithm and also improve the existence guarantee to a factor of (3/4 + min(1/36, 3/(16n-4))). For small n, this provides a noticeable improvement. Furthermore, we present a tight example of this algorithm, showing that this may be the best factor one can hope for with the current techniques.","doi":"10.24963/ijcai.2023/276","url":"https://ijcai.org/proceedings/2023/276","pdf":"https://ijcai.org/proceedings/2023/0276.pdf","markdown":"https://ijcai.org/proceedings/2023/276.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/276","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":276,"pages":{"first":2485,"last":2493},"keywords":["Agent-based and Multi-agent Systems: MAS: Resource allocation","Game Theory and Economic Paradigms: GTEP: Computational social choice","Game Theory and Economic Paradigms: GTEP: Fair division"],"videos":[],"references":[{"position":1,"raw":"[Akrami et al., 2023] Hannaneh Akrami, Jugal Garg, Eklavya Sharma, and Setareh Taki. 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