Improved Maximin Share Guarantee for Additive Valuations

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 $1 - \frac{1}{n^4}$ of maximin share value to all agents. However, the best currently known algorithm achieves an approximation guarantee of $\frac{3}{4} + \frac{3}{3836}$ for $\textsf{MMS}$. In this work, we narrow this gap and improve the best-known approximation guarantee for $\textsf{MMS}$ to $\frac{10}{13}$.