Efficient Analysis to Protect Control into Critical Infrastructures

To protect control into critical infrastructures against single component-dependency attacks or failures, we analyse the importance of any given dependency in maintaining controllability with a minimum set of inputs. Since people use critical, redundant and ordinary categories to clarify how an edge maintains controllability of linear time-invariant(LTI) dynamical networks, according to graph-based models of infrastructures and the minimum input theorem, we firstly use a ErdHos-Renyi random digraph with a precomputed maximum matching to model some LTI and controllable infrastructures by a minimum set of inputs. We then efficiently analyse any given arc's category before and during single-arc removals, as a way to further confirm how related dependency keeps control into infrastructures. After running our label operations with linear time and space complexity, any edge-category analysis can be thus executed in $O(1)$ time in both cases.