Distributed Inference Networks with Costly Wires

Distributed control systems are physical constructs, incurring deployment and maintenance costs for their communication infrastructure. Inference is a central function of many distributed control systems. This paper formulates and studies the tradeoff between algebraic notions of inference functionality and algebraic notions of wiring costs. It is shown that separated topology design and node placement yields optimal network design. This design problem is shown to be NP-complete, but is carried out for small network size. A natural relaxation is shown to be a reverse convex minimization problem.