New algorithm boosts fair resource allocation guarantee to golden ratio
Researchers achieve (φ-1) approximation for groupwise maximin share fairness, beating previous 4/7 bound.
A team of computer scientists (Georgios Amanatidis, Anna Korfiati, Evangelos Markakis, Christodoulos Santorinaios) has published a new paper on arXiv that significantly improves the theoretical guarantees for fair division of indivisible goods. The work focuses on groupwise maximin share fairness (GMMS), a rigorous fairness notion requiring each agent’s allocation to be comparable to their maximin share — calculated against any subset of agents containing them. The authors present a polynomial-time algorithm achieving a (φ-1) ≈ 0.618 approximation, where φ is the golden ratio (1.618). This beats the previous best known bound of 4/7 (~0.571) from Chaudhury et al. (2021) and Amanatidis et al. (2020).
The algorithm builds on the Draft-and-Eliminate framework but introduces a tighter analysis of the value within any subinstance induced by restricting the allocation to a subset of agents. The analysis is asymptotically tight for algorithms sharing these properties. Additionally, the paper provides improved guarantees for special cases: when all agents agree on the top n goods or when the number of agents is small. For the specific case of three agents, they achieve an approximation of (√10–1)/3 ≈ 0.72 by partially characterizing maximin share guarantees for short picking sequences. The work is 29 pages with 2 figures and appears in arXiv:2606.04731.
- Improves GMMS approximation from 4/7 (~0.571) to (φ-1) ≈ 0.618 using a polynomial-time algorithm
- Achieves 0.72 approximation for three-agent cases via short picking sequences
- Analysis is asymptotically tight for algorithms based on the Draft-and-Eliminate method
Why It Matters
Strengthens theoretical foundations for fair AI resource allocation—critical for multi-agent systems, cloud computing, and automated negotiation.