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

TL;DR

This paper introduces a new, simpler algorithm that improves the approximation ratio for maximin share allocations of indivisible goods to 7/9, and provides an FPTAS for near-optimal solutions within specified error bounds.

Contribution

The paper presents a novel analytical framework and an improved, simpler algorithm achieving a 7/9 approximation ratio and an FPTAS for maximin share allocations.

Findings

Achieved a 7/9 approximation ratio for MMS allocations.

Developed an FPTAS that approximates within 7/9 - ε in polynomial time.

Simplified the algorithm compared to prior methods.

Abstract

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.