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

Distributed Submodular Maximization with Limited Information