# Deterministic Algorithms for Submodular Maximization Problems

arXiv: https://arxiv.org/abs/1508.02157 · HTML: https://mlsanity.com/paper/1508.02157/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Aug 2015.

## Built on by (most cited first, 10 of 10)

- [Online Learning via Offline Greedy Algorithms: Applications in Market Design and Optimization](https://mlsanity.com/paper/2102.11050/) (2021)
- [Submodularity In Machine Learning and Artificial Intelligence](https://mlsanity.com/paper/2202.00132/) (2022)
- [Randomized Greedy Learning for Non-monotone Stochastic Submodular Maximization Under Full-bandit Feedback](https://mlsanity.com/paper/2302.01324/) (2023)
- [Submodular Minimax Optimization: Finding Effective Sets](https://mlsanity.com/paper/2305.16903/) (2023)
- [Some Inapproximability Results of MAP Inference and Exponentiated Determinantal Point Processes](https://mlsanity.com/paper/2109.00727/) (2021)
- [Online Learning for Non-monotone Submodular Maximization: From Full Information to Bandit Feedback](https://mlsanity.com/paper/2208.07632/) (2022)
- [Contextual Combinatorial Bandits with Changing Action Sets via Gaussian Processes](https://mlsanity.com/paper/2110.02248/) (2021)
- [The Cost of Consistency: Submodular Maximization with Constant Recourse](https://mlsanity.com/paper/2412.02492/) (2024)
- [A Note On Deterministic Submodular Maximization With Bounded Curvature](https://mlsanity.com/paper/2409.02943/) (2024)
- [Allocating Variance to Maximize Expectation](https://mlsanity.com/paper/2502.18463/) (2025)

## Abstract (arXiv)

Randomization is a fundamental tool used in many theoretical and practical areas of computer science. We study here the role of randomization in the area of submodular function maximization. In this area most algorithms are randomized, and in almost all cases the approximation ratios obtained by current randomized algorithms are superior to the best results obtained by known deterministic algorithms. Derandomization of algorithms for general submodular function maximization seems hard since the access to the function is done via a value oracle. This makes it hard, for example, to apply standard derandomization techniques such as conditional expectations. Therefore, an interesting fundamental problem in this area is whether randomization is inherently necessary for obtaining good approximation ratios. In this work we give evidence that randomization is not necessary for obtaining good algorithms by presenting a new technique for derandomization of algorithms for submodular function maximization. Our high level idea is to maintain explicitly a (small) distribution over the states of the algorithm, and carefully update it using marginal values obtained from an extreme point solution of a suitable linear formulation. We demonstrate our technique on two recent algorithms for unconstrained submodular maximization and for maximizing submodular function subject to a cardinality constraint. In particular, for unconstrained submodular maximization we obtain an optimal deterministic 1/2-approximation showing that randomization is unnecessary for obtaining optimal results for this setting.