# Distributed Submodular Maximization with Limited Information

## TL;DR

This paper studies how limited information sharing among agents affects the effectiveness of greedy algorithms in distributed submodular maximization, providing bounds based on graph properties and validating with simulations.

## Contribution

It introduces bounds on greedy algorithm performance considering information constraints, linking them to graph-theoretic properties like clique and chromatic numbers.

## Key findings

- Lower bounds depend on the clique number of the information graph.
- Upper bounds are characterized by the chromatic number of the graph.
- Simulations confirm the theoretical bounds across various network models.

## Abstract

We consider a class of distributed submodular maximization problems in which each agent must choose a single strategy from its strategy set. The global objective is to maximize a submodular function of the strategies chosen by each agent. When choosing a strategy, each agent has access to only a limited number of other agents' choices. For each of its strategies, an agent can evaluate its marginal contribution to the global objective given its information. The main objective is to investigate how this limitation of information about the strategies chosen by other agents affects the performance when agents make choices according to a local greedy algorithm. In particular, we provide lower bounds on the performance of greedy algorithms for submodular maximization, which depend on the clique number of a graph that captures the information structure. We also characterize graph-theoretic upper bounds in terms of the chromatic number of the graph. Finally, we demonstrate how certain graph properties limit the performance of the greedy algorithm. Simulations on several common models for random networks demonstrate our results.