  The submodular maximization problem is widely applicable in many engineering
problems where objectives exhibit diminishing returns. While this problem is
known to be NP-hard for certain subclasses of objective functions, there is a
greedy algorithm which guarantees approximation at least 1/2 of the optimal
solution. This greedy algorithm can be implemented with a set of agents, each
making a decision sequentially based on the choices of all prior agents. In
this paper, we consider a generalization of the greedy algorithm in which
agents can make decisions in parallel, rather than strictly in sequence. In
particular, we are interested in partitioning the agents, where a set of agents
in the partition all make a decision simultaneously based on the choices of
prior agents, so that the algorithm terminates in limited iterations. We
provide bounds on the performance of this parallelized version of the greedy
algorithm and show that dividing the agents evenly among the sets in the
partition yields an optimal structure. We additionally show that this optimal
structure is still near-optimal when the objective function exhibits a certain
monotone property. Lastly, we show that the same performance guarantees can be
achieved in the parallelized greedy algorithm even when agents can only observe
the decisions of a subset of prior agents.

Distributed, Parallel, and Cluster Computing;Multiagent Systems;Systems and Control;Systems and Control