# The Impact of Information in Greedy Submodular Maximization

arXiv: https://arxiv.org/abs/1807.10639 · HTML: https://mlsanity.com/paper/1807.10639/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jul 2018.

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

- [Resource-Aware Distributed Submodular Maximization: A Paradigm for Multi-Robot Decision-Making](https://mlsanity.com/paper/2204.07520/) (2022)
- [Bandit Submodular Maximization for Multi-Robot Coordination in Unpredictable and Partially Observable Environments](https://mlsanity.com/paper/2305.12795/) (2023)
- [Online Submodular Coordination with Bounded Tracking Regret: Theory, Algorithm, and Applications to Multi-Robot Coordination](https://mlsanity.com/paper/2209.12429/) (2022)
- [Communication- and Computation-Efficient Distributed Submodular Optimization in Robot Mesh Networks](https://mlsanity.com/paper/2407.10382/) (2024)
- [Leveraging Untrustworthy Commands for Multi-Robot Coordination in Unpredictable Environments: A Bandit Submodular Maximization Approach](https://mlsanity.com/paper/2309.16161/) (2023)
- [Performance-Aware Self-Configurable Multi-Agent Networks: A Distributed Submodular Approach for Simultaneous Coordination and Network Design](https://mlsanity.com/paper/2409.01411/) (2024)
- [Distributed Online Submodular Maximization under Communication Delays: A Simultaneous Decision-Making Approach](https://mlsanity.com/paper/2603.27803/) (2026)

## Abstract (arXiv)

The maximization of submodular functions is an NP-Hard problem for certain subclasses of functions, for which a simple greedy algorithm has been shown to guarantee a solution whose quality is within 1/2 of the optimal. When this algorithm is implemented in a distributed way, agents sequentially make decisions based on the decisions of all previous agents. This work explores how limited access to the decisions of previous agents affects the quality of the solution of the greedy algorithm. Specifically, we provide tight upper and lower bounds on how well the algorithm performs, as a function of the information available to each agent. Intuitively, the results show that performance roughly degrades proportionally to the size of the largest group of agents which make decisions independently. Additionally, we consider the case where a system designer is given a set of agents and a global limit on the amount of information that can be accessed. Our results show that the best designs partition the agents into equally-sized sets and allow agents to access the decisions of all previous agents within the same set.