# Streaming Submodular Maximization under a k-Set System Constraint

arXiv: https://arxiv.org/abs/2002.03352 · HTML: https://mlsanity.com/paper/2002.03352/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2020.

## Built on by (most cited first, 3 of 3)

- [The Power of Subsampling in Submodular Maximization](https://mlsanity.com/paper/2104.02772/) (2021)
- [Submodular Maximization under the Intersection of Matroid and Knapsack Constraints](https://mlsanity.com/paper/2307.09487/) (2023)
- [Practical Parallel Algorithms for Non-Monotone Submodular Maximization](https://mlsanity.com/paper/2308.10656/) (2023)

## Abstract (arXiv)

In this paper, we propose a novel framework that converts streaming algorithms for monotone submodular maximization into streaming algorithms for non-monotone submodular maximization. This reduction readily leads to the currently tightest deterministic approximation ratio for submodular maximization subject to a k-matchoid constraint. Moreover, we propose the first streaming algorithm for monotone submodular maximization subject to k-extendible and k-set system constraints. Together with our proposed reduction, we obtain O(klog k) and O(k2log k) approximation ratio for submodular maximization subject to the above constraints, respectively. We extensively evaluate the empirical performance of our algorithm against the existing work in a series of experiments including finding the maximum independent set in randomly generated graphs, maximizing linear functions over social networks, movie recommendation, Yelp location summarization, and Twitter data summarization.