# The One-way Communication Complexity of Submodular Maximization with Applications to Streaming and Robustness

arXiv: https://arxiv.org/abs/2003.13459 · HTML: https://mlsanity.com/paper/2003.13459/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2020.

## Built on by (most cited first, 7 of 7)

- [Fully Dynamic Submodular Maximization over Matroids](https://mlsanity.com/paper/2305.19918/) (2023)
- [On the Complexity of Dynamic Submodular Maximization](https://mlsanity.com/paper/2111.03198/) (2021)
- [Fairness in Streaming Submodular Maximization over a Matroid Constraint](https://mlsanity.com/paper/2305.15118/) (2023)
- [Fairness in Submodular Maximization over a Matroid Constraint](https://mlsanity.com/paper/2312.14299/) (2023)
- [The Cost of Consistency: Submodular Maximization with Constant Recourse](https://mlsanity.com/paper/2412.02492/) (2024)
- [A General Framework for Dynamic Consistent Submodular Maximization](https://mlsanity.com/paper/2606.04946/) (2026)
- [Streaming Submodular Maximization with Differential Privacy](https://mlsanity.com/paper/2210.14315/) (2022)

## Abstract (arXiv)

We consider the classical problem of maximizing a monotone submodular function subject to a cardinality constraint, which, due to its numerous applications, has recently been studied in various computational models. We consider a clean multi-player model that lies between the offline and streaming model, and study it under the aspect of one-way communication complexity. Our model captures the streaming setting (by considering a large number of players), and, in addition, two player approximation results for it translate into the robust setting. We present tight one-way communication complexity results for our model, which, due to the above-mentioned connections, have multiple implications in the data stream and robust setting. Even for just two players, a prior information-theoretic hardness result implies that no approximation factor above 1/2 can be achieved in our model, if only queries to feasible sets are allowed. We show that the possibility of querying infeasible sets can actually be exploited to beat this bound, by presenting a tight 2/3-approximation taking exponential time, and an efficient 0.514-approximation. To the best of our knowledge, this is the first example where querying a submodular function on infeasible sets leads to provably better results. Through the above-mentioned link to the robust setting, both of these algorithms improve on the current state-of-the-art for robust submodular maximization, showing that approximation factors beyond 1/2 are possible. Moreover, exploiting the link of our model to streaming, we settle the approximability for streaming algorithms by presenting a tight 1/2+varepsilon hardness result, based on the construction of a new family of coverage functions. This improves on a prior 1-1/e+varepsilon hardness and matches, up to an arbitrarily small margin, the best known approximation algorithm.