# Cardinality constrained submodular maximization for random streams

arXiv: https://arxiv.org/abs/2111.07217 · HTML: https://mlsanity.com/paper/2111.07217/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2021.

## Built on by (most cited first, 2 of 2)

- [Fully Dynamic Submodular Maximization over Matroids](https://mlsanity.com/paper/2305.19918/) (2023)
- [Optimal Data Selection: An Online Distributed View](https://mlsanity.com/paper/2201.10547/) (2022)

## Abstract (arXiv)

We consider the problem of maximizing submodular functions in single-pass streaming and secretaries-with-shortlists models, both with random arrival order. For cardinality constrained monotone functions, Agrawal, Shadravan, and Stein gave a single-pass (1-1/e-varepsilon)-approximation algorithm using only linear memory, but their exponential dependence on varepsilon makes it impractical even for varepsilon=0.1. We simplify both the algorithm and the analysis, obtaining an exponential improvement in the varepsilon-dependence (in particular, O(k/varepsilon) memory). Extending these techniques, we also give a simple (1/e-varepsilon)-approximation for non-monotone functions in O(k/varepsilon) memory. For the monotone case, we also give a corresponding unconditional hardness barrier of 1-1/e+varepsilon for single-pass algorithms in randomly ordered streams, even assuming unlimited computation. Finally, we show that the algorithms are simple to implement and work well on real world datasets.