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We study fair division of indivisible chores among n agents with additive cost functions using the popular fairness notion of maximin share (MMS). Since MMS allocations do not always exist for more than two agents, the goal has been to improve its approximations and identify interesting special cases where MMS allocations exist. We show the existence of· 1-out-of-9n/11 MMS allocations, which improves the state-of-the-art factor of 1-out-of-3n/4.· MMS allocations for factored instances, which resolves an open question posed by Ebadian et al. (2021).· 15/13-MMS allocations for personalized bivalued instances, improving the state-of-the-art factor of 13/11.We achieve these results by leveraging the HFFD algorithm of Huang and Lu (2021). Our approach also provides polynomial-time algorithms for computing an MMS allocation for factored instances and a 15/13-MMS allocation for personalized bivalued instances.
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Simplification and Improvement of MMS Approximation
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.
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- Award ID(s):
- 1942321
- PAR ID:
- 10491684
- Publisher / Repository:
- International Joint Conferences on Artificial Intelligence Organization
- Date Published:
- ISBN:
- 978-1-956792-03-4
- Page Range / eLocation ID:
- 2485 to 2493
- Format(s):
- Medium: X
- Location:
- Macau, SAR China
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Conference Paper:
- https://doi.org/10.24963/ijcai.2023/276
