"Sometimes There is No Most-Vital" Arc: Assessing and Improving the Operational Resilience of Systems

Abstract : This paper shows that no simple common-sense rule of thumb can be used to identify a most-vital arc even in a simple maximum-flow problem. The correct answer requires analysis equivalent in difficulty to completely solving the maximum-flow problem, perhaps repeatedly. This insight generalizes to finding a most-vital component, or set of components in a system whose operation is described by a more general model. Our paper shows how to evaluate the criticality of sets of components, how to assess the worst-case set of components that might be lost to a given number of simultaneous hostile attacks (or engineering failures, or losses to Mother Nature), and how to allocate limited defensive resources to minimize the maximum damage from a subsequent attack. Collateral insights include the fact that there is no way to prioritize individual components by criticality, and that the analysis that determines critical component sets also yields objective assessments of operational system resilience and can provide constructive advice on how to increase it.