# Parallel Algorithm for Non-Monotone DR-Submodular Maximization

arXiv: https://arxiv.org/abs/1905.13272 · HTML: https://mlsanity.com/paper/1905.13272/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2019.

## Built on by (most cited first, 9 of 9)

- [Submodular + Concave](https://mlsanity.com/paper/2106.04769/) (2021)
- [Submodular Maximization subject to a Knapsack Constraint: Combinatorial Algorithms with Near-optimal Adaptive Complexity](https://mlsanity.com/paper/2102.08327/) (2021)
- [Best of Both Worlds: Practical and Theoretically Optimal Submodular Maximization in Parallel](https://mlsanity.com/paper/2111.07917/) (2021)
- [Lazy and Fast Greedy MAP Inference for Determinantal Point Process](https://mlsanity.com/paper/2206.05947/) (2022)
- [Greedy Bayesian Posterior Approximation with Deep Ensembles](https://mlsanity.com/paper/2105.14275/) (2021)
- [Scalable Distributed Algorithms for Size-Constrained Submodular Maximization in the MapReduce and Adaptive Complexity Models](https://mlsanity.com/paper/2206.09563/) (2022)
- [Practical Parallel Algorithms for Non-Monotone Submodular Maximization](https://mlsanity.com/paper/2308.10656/) (2023)
- [Improved Parallel Algorithm for Non-Monotone Submodular Maximization under Knapsack Constraint](https://mlsanity.com/paper/2409.04415/) (2024)
- [Fast Approximation Algorithm for Non-Monotone DR-submodular Maximization under Size Constraint](https://mlsanity.com/paper/2511.02254/) (2025)

## Abstract (arXiv)

In this work, we give a new parallel algorithm for the problem of maximizing a non-monotone diminishing returns submodular function subject to a cardinality constraint. For any desired accuracy ε, our algorithm achieves a 1/e - ε approximation using O(logn log(1/ε) / ε3) parallel rounds of function evaluations. The approximation guarantee nearly matches the best approximation guarantee known for the problem in the sequential setting and the number of parallel rounds is nearly-optimal for any constant ε. Previous algorithms achieve worse approximation guarantees using Omega(log2n) parallel rounds. Our experimental evaluation suggests that our algorithm obtains solutions whose objective value nearly matches the value obtained by the state of the art sequential algorithms, and it outperforms previous parallel algorithms in number of parallel rounds, iterations, and solution quality.