# Fully Dynamic Algorithm for Constrained Submodular Optimization

arXiv: https://arxiv.org/abs/2006.04704 · HTML: https://mlsanity.com/paper/2006.04704/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2020.

## Built on by (most cited first, 11 of 11)

- [Submodular Maximization subject to a Knapsack Constraint: Combinatorial Algorithms with Near-optimal Adaptive Complexity](https://mlsanity.com/paper/2102.08327/) (2021)
- [Deletion Robust Submodular Maximization over Matroids](https://mlsanity.com/paper/2201.13128/) (2022)
- [Fully Dynamic Submodular Maximization over Matroids](https://mlsanity.com/paper/2305.19918/) (2023)
- [Dynamic Algorithms for Matroid Submodular Maximization](https://mlsanity.com/paper/2306.00959/) (2023)
- [On the Complexity of Dynamic Submodular Maximization](https://mlsanity.com/paper/2111.03198/) (2021)
- [Deletion Robust Non-Monotone Submodular Maximization over Matroids](https://mlsanity.com/paper/2208.07582/) (2022)
- [Consistent Submodular Maximization](https://mlsanity.com/paper/2405.19977/) (2024)
- [The Cost of Consistency: Submodular Maximization with Constant Recourse](https://mlsanity.com/paper/2412.02492/) (2024)
- [Dynamic Non-monotone Submodular Maximization](https://mlsanity.com/paper/2311.03685/) (2023)
- [A General Framework for Dynamic Consistent Submodular Maximization](https://mlsanity.com/paper/2606.04946/) (2026)
- [A Dynamic Algorithm for Weighted Submodular Cover Problem](https://mlsanity.com/paper/2407.10003/) (2024)

## Abstract (arXiv)

The task of maximizing a monotone submodular function under a cardinality constraint is at the core of many machine learning and data mining applications, including data summarization, sparse regression and coverage problems. We study this classic problem in the fully dynamic setting, where elements can be both inserted and removed. Our main result is a randomized algorithm that maintains an efficient data structure with a poly-logarithmic amortized update time and yields a (1/2-ε)-approximate solution. We complement our theoretical analysis with an empirical study of the performance of our algorithm.