  We consider a class of discrete optimization problems that aim to maximize a
submodular objective function subject to a distributed partition matroid
constraint. More precisely, we consider a networked scenario in which multiple
agents choose actions from local strategy sets with the goal of maximizing a
submodular objective function defined over the set of all possible actions.
Given this distributed setting, we develop Constraint-Distributed Continuous
Greedy (CDCG), a message passing algorithm that converges to the tight
$(1-1/e)$ approximation factor of the optimum global solution using only local
computation and communication. It is known that a sequential greedy algorithm
can only achieve a $1/2$ multiplicative approximation of the optimal solution
for this class of problems in the distributed setting. Our framework relies on
lifting the discrete problem to a continuous domain and developing a consensus
algorithm that achieves the tight $(1-1/e)$ approximation guarantee of the
global discrete solution once a proper rounding scheme is applied. We also
offer empirical results from a multi-agent area coverage problem to show that
the proposed method significantly outperforms the state-of-the-art sequential
greedy method.
