# Dynamic Constrained Submodular Optimization with Polylogarithmic Update Time

arXiv: https://arxiv.org/abs/2305.15192 · HTML: https://mlsanity.com/paper/2305.15192/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2023.

## Built on by (most cited first, 5 of 5)

- [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)
- [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)

Maximizing a monotone submodular function under cardinality constraint k is a core problem in machine learning and database with many basic applications, including video and data summarization, recommendation systems, feature extraction, exemplar clustering, and coverage problems. We study this classic problem in the fully dynamic model where a stream of insertions and deletions of elements of an underlying ground set is given and the goal is to maintain an approximate solution using a fast update time. A recent paper at NeurIPS'20 by Lattanzi, Mitrovic, Norouzi-Fard, Tarnawski, Zadimoghaddam claims to obtain a dynamic algorithm for this problem with a frac12 -ε approximation ratio and a query complexity bounded by poly(log(n),log(k),ε-1). However, as we explain in this paper, the analysis has some important gaps. Having a dynamic algorithm for the problem with polylogarithmic update time is even more important in light of a recent result by Chen and Peng at STOC'22 who show a matching lower bound for the problem -- any randomized algorithm with a frac12+ε approximation ratio must have an amortized query complexity that is polynomial in n. In this paper, we develop a simpler algorithm for the problem that maintains a (frac12-ε)-approximate solution for submodular maximization under cardinality constraint k using a polylogarithmic amortized update time.