  In this letter we discuss cost optimization of sensor networks monitoring
structurally full-rank systems under distributed observability constraint.
Using structured systems theory, the problem is relaxed into two subproblems:
(i) sensing cost optimization and (ii) networking cost optimization. Both
problems are reformulated as combinatorial optimization problems. The sensing
cost optimization is shown to have a polynomial order solution. The networking
cost optimization is shown to be NP-hard in general, but has a polynomial order
solution under specific conditions. A 2-approximation polynomial order
relaxation is provided for general networking cost optimization, which is
applicable in large-scale system monitoring.
