Energy preserving matching of sensor network topology to dependency graph of the observed field

The goal of this paper is to design the topology of a wireless sensor network observing a Markov random field in order to match the structure of the dependency graph of the observed field, under constraints on the energy spent to maintain the sensor network connectivity. The approach is important to enable the implementation of belief propagation algorithms at the network level, to achieve optimal decisions requiring simple message passing mechanisms among nearby nodes. Our main task is to recover the sparsity of the dependency graph and to replicate it at the sensor network level, under the constraint of limiting the transmit power necessary to establish the link among the nodes. To avoid the computational burden of the combinatorial problem associated to the topology design, we devise ad hoc relaxation techniques that allow us to achieve the solution through efficient algorithms based on difference of convex problems.