Decentralized detection with long-distance communication

We consider the well-studied decentralized Bayesian detection problem with the twist that a small subset of nodes (all arranged in a given directed network topology) may also communicate to "long-distance" neighbors via an overlay undirected network topology. Providing a certain condition on the interface between the two networks is upheld, the natural combination of the efficient team solutions already known for each type of network alone remains team-optimal in the combined network.