# A Poisson Process for Submodular Maximization

arXiv: https://arxiv.org/abs/2605.03071 · HTML: https://mlsanity.com/paper/2605.03071/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2026.

## Built on by (most cited first, 2 of 2)

- [Adversarial Resilience of Poisson-Process Submodular Maximization over Matroids, and Full-Bandit Learning](https://mlsanity.com/paper/2608.12134/) (2026)
- [Bandit Submodular Maximization under Matroid Constraints: Learning Compressed Exchange Policy](https://mlsanity.com/paper/2608.24627/) (2026)

## Abstract (arXiv)

We study the problem of maximizing a monotone submodular function subject to a matroid independence constraint. For more than a decade, a rich body of work has studied this problem. Initially, a tight approximation of  (1-frac1e) was given using the continuous greedy algorithm [Calinescu-Chekuri-Pal-Vondr'ak STOC`2008] and later non-oblivious local search techniques were able to match this tight approximation guarantee [Filmus-Ward FOCS`2012] and [Buchbinder-Feldman FOCS`2024]. We propose a new and remarkably simple approach to this problem that is based on a stochastic Poisson process. Our approach matches the tight  (1-frac1e) approximation guarantee and it differs from the known two techniques since it does not require discretization or rounding while performing very few single element swaps. We also present applications of our approach and obtain fast algorithms for submodular welfare maximization, and for the general and separable assignment problems.