# APX-Hardness of Maximizing Nash Social Welfare with Indivisible Items

arXiv: https://arxiv.org/abs/1507.01159 · HTML: https://mlsanity.com/paper/1507.01159/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jul 2015.

## Built on by (most cited first, 3 of 3)

- [Welfare and Fairness in Multi-objective Reinforcement Learning](https://mlsanity.com/paper/2212.01382/) (2022)
- [PROPm Allocations of Indivisible Goods to Multiple Agents](https://mlsanity.com/paper/2105.11348/) (2021)
- [EF1-Constrained Nash Social Welfare with Identical Additive Valuations: Complexity, Guarantees, and Experiments](https://mlsanity.com/paper/2609.03846/) (2026)

## Abstract (arXiv)

We study the problem of allocating a set of indivisible items to agents with additive utilities to maximize the Nash social welfare. Cole and Gkatzelis recently proved that this problem admits a constant factor approximation. We complement their result by showing that this problem is APX-hard.