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arXiv · 2510.10423

Improved Maximin Share Guarantee for Additive Valuations

Ehsan Heidari·Alireza Kaviani·Masoud Seddighin·AmirMohammad Shahrezaei
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Abstract

The maximin share ($\textsf{MMS}$) is the most prominent share-based fairness notion in the fair allocation of indivisible goods. Recent years have seen significant efforts to improve the approximation guarantees for $\textsf{MMS}$ for different valuation classes, particularly for additive valuations. For the additive setting, it has been shown that for some instances, no allocation can guarantee a factor better than $1-\tfrac{1}{n^4}$ of maximin share value to all agents. However, the best currently known algorithm achieves an approximation guarantee of $\tfrac{3}{4} + \tfrac{3}{3836}$ for $\textsf{MMS}$. In this work, we narrow this gap and improve the best-known approximation guarantee for $\textsf{MMS}$ to $\tfrac{10}{13}$.

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Ehsan Heidari, Alireza Kaviani, Masoud Seddighin, AmirMohammad Shahrezaei. 2025-10-12. Improved Maximin Share Guarantee for Additive Valuations. https://arxiv.org/abs/2510.10423

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