Distributed Submodular Maximization with Bounded Communication Cost

We study distributed submodular maximization in networks with heterogeneous communication costs. In the distributed maximization algorithm, each agent selects a strategy from a discrete set of options, and the objective is to maximize a global submodular function over these strategies. The network topology imposes limitations on information sharing, and several recent works have derived bounds on the performance of the algorithm in terms of graph properties. In this work, we consider the problem of designing a network that maximizes the algorithm performance subject to a bound on the total communication cost of the algorithm execution. We first prove that this network design problem is NP-hard. We then present an approximation algorithm for it. Next, we show that the algorithm communication cost can be further reduced by using multi-hop routing for information propagation. We give a polynomial-time algorithm that finds the optimal information propagation scheme for the distributed algorithm in edge-weighted networks. Finally, we present experimental results highlighting the performance of our algorithms.