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.
Categories: cs.GT cs.DS