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arXiv · 2511.13056

An FPTAS for 7/9-Approximation to Maximin Share Allocations

Xin Huang·Shengwei Zhou
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Abstract

We present a new algorithm that achieves a $\frac{7}{9}$-approximation for the \emph{maximin share (MMS)} allocation of indivisible goods under additive valuations, improving the current best ratio of $\frac{10}{13}$~\cite{conf/soda/HeidariKSS26}. Building on a new analytical framework, we further obtain an FPTAS that achieves a $\frac{7}{9}-\varepsilon$ approximation in $\tfrac{1}{\varepsilon} \cdot \mathrm{poly}(n,m)$ time. The main technical ingredient is a dynamic witness-allocation framework that certifies adaptive reductions throughout the allocation process.

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Xin Huang, Shengwei Zhou. 2026-09-07. An FPTAS for 7/9-Approximation to Maximin Share Allocations. https://arxiv.org/abs/2511.13056

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