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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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Improved MMS Approximations for Few Agent Types
We study fair division of indivisible goods under the maximin share (MMS) fairness criterion in settings where agents are grouped into a small number of types, with agents within each type having identical valuations. For the special case of a single type, an exact MMS allocation is always guaranteed to exist. However, for two or more distinct agent types, exact MMS allocations do not always exist, shifting the focus to establishing the existence of approximate-MMS allocations. A series of works over the last decade has resulted in the best-known approximation guarantee of 3/4 + 3/3836. In this paper, we improve the approximation guarantees for settings where agents are grouped into two or three types, a scenario that arises in many practical settings. Specifically, we present novel algorithms that guarantee a 4/5-MMS allocation for two agent types and a 16/21-MMS allocation for three agent types. Our approach leverages the MMS partition of the majority type and adapts it to provide improved fairness guarantees for all types.
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- Award ID(s):
- 2334461
- PAR ID:
- 10660805
- Publisher / Repository:
- International Joint Conferences on Artificial Intelligence Organization
- Date Published:
- Page Range / eLocation ID:
- 4057 to 4064
- Format(s):
- Medium: X
- 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.2025/452
