Simplification and Improvement of MMS Approximation

Hannaneh Akrami, Jugal Garg, Eklavya Sharma, Setareh Taki

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish (US)
Title of host publicationProceedings of the 32nd International Joint Conference on Artificial Intelligence, IJCAI 2023
EditorsEdith Elkind
PublisherInternational Joint Conferences on Artificial Intelligence
Number of pages9
ISBN (Electronic)9781956792034
StatePublished - 2023
Event32nd International Joint Conference on Artificial Intelligence, IJCAI 2023 - Macao, China
Duration: Aug 19 2023Aug 25 2023

Publication series

NameIJCAI International Joint Conference on Artificial Intelligence
ISSN (Print)1045-0823


Conference32nd International Joint Conference on Artificial Intelligence, IJCAI 2023

ASJC Scopus subject areas

  • Artificial Intelligence


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