# Dynamic Non-monotone Submodular Maximization

arXiv: https://arxiv.org/abs/2311.03685 · HTML: https://mlsanity.com/paper/2311.03685/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 51 references that are in the map.
- First posted on arXiv 7 Nov 2023.

## Builds on (most cited first, 17 of 17)

- [Restricted Strong Convexity Implies Weak Submodularity](https://mlsanity.com/paper/1612.00804/) (2016)
- [Scalable Greedy Feature Selection via Weak Submodularity](https://mlsanity.com/paper/1703.02723/) (2017)
- [Constrained Submodular Maximization via a Non-symmetric Technique](https://mlsanity.com/paper/1611.03253/) (2016)
- [Streaming Non-monotone Submodular Maximization: Personalized Video Summarization on the Fly](https://mlsanity.com/paper/1706.03583/) (2017)
- [Non-monotone Submodular Maximization with Nearly Optimal Adaptivity and Query Complexity](https://mlsanity.com/paper/1808.06932/) (2018)
- [Do Less, Get More: Streaming Submodular Maximization with Subsampling](https://mlsanity.com/paper/1802.07098/) (2018)
- [Beyond 1/2-Approximation for Submodular Maximization on Massive Data Streams](https://mlsanity.com/paper/1808.01842/) (2018)
- [Fully Dynamic Algorithm for Constrained Submodular Optimization](https://mlsanity.com/paper/2006.04704/) (2020)
- [Non-monotone Submodular Maximization in Exponentially Fewer Iterations](https://mlsanity.com/paper/1807.11462/) (2018)
- [Submodular Optimization in the MapReduce Model](https://mlsanity.com/paper/1810.01489/) (2018)
- [Streaming Algorithms for Submodular Function Maximization](https://mlsanity.com/paper/1504.08024/) (2015)
- [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 Influence Maximization](https://mlsanity.com/paper/2110.12602/) (2021)
- [Practical and Parallelizable Algorithms for Non-Monotone Submodular Maximization with Size Constraint](https://mlsanity.com/paper/2009.01947/) (2020)
- [On the Complexity of Dynamic Submodular Maximization](https://mlsanity.com/paper/2111.03198/) (2021)
- [Dynamic Constrained Submodular Optimization with Polylogarithmic Update Time](https://mlsanity.com/paper/2305.15192/) (2023)

## Built on by (most cited first, 1 of 1)

- [A Dynamic Algorithm for Weighted Submodular Cover Problem](https://mlsanity.com/paper/2407.10003/) (2024)

## Abstract (arXiv)

Maximizing submodular functions has been increasingly used in many applications of machine learning, such as data summarization, recommendation systems, and feature selection. Moreover, there has been a growing interest in both submodular maximization and dynamic algorithms. In 2020, Monemizadeh and Lattanzi, Mitrovic, Norouzi-Fard, Tarnawski, and Zadimoghaddam initiated developing dynamic algorithms for the monotone submodular maximization problem under the cardinality constraint k. Recently, there have been some improvements on the topic made by Banihashem, Biabani, Goudarzi, Hajiaghayi, Jabbarzade, and Monemizadeh. In 2022, Chen and Peng studied the complexity of this problem and raised an important open question: "Can we extend [fully dynamic] results (algorithm or hardness) to non-monotone submodular maximization?". We affirmatively answer their question by demonstrating a reduction from maximizing a non-monotone submodular function under the cardinality constraint k to maximizing a monotone submodular function under the same constraint. Through this reduction, we obtain the first dynamic algorithms to solve the non-monotone submodular maximization problem under the cardinality constraint k. Our algorithms maintain an (8+ε)-approximate of the solution and use expected amortized O(ε-3k3log3(n)log(k)) or O(ε-1k2log3(k)) oracle queries per update, respectively. Furthermore, we showcase the benefits of our dynamic algorithm for video summarization and max-cut problems on several real-world data sets.