We present a new algorithm that achieves a $\frac{7}{9}$-approximation for the maximin share (MMS) allocation of indivisible goods under additive valuations, improving the current best ratio of $\frac{10}{13}$ (Heidari et al., SODA 2026). 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. Compared with prior work (Heidari et al., SODA 2026), our algorithm is substantially simpler.

翻译：我们提出了一种新算法，在加性估值下对不可分割物品的最大最小份额（MMS）分配实现了7/9近似比，改进了当前10/13的最佳比率（Heidari等人，SODA 2026）。基于新的分析框架，我们进一步得到了一个FPTAS，可在(1/ε)·poly(n,m)时间内实现7/9-ε近似。与先前工作（Heidari等人，SODA 2026）相比，我们的算法显著简化。