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Infrastructure systems, such as power systems, often experience cascadingfailures. Modeling an infrastructure system as a collection of interdependentnetworks has recently received attention as a way to explain cascadingfailures. In this study, we propose an approach to find the set of criticalnodes in an interdependent network. For an integer k, we say that a set of knodes is critical if the initial failures of these k nodes result in the mostsevere cascading failure among all sets of k nodes. This approach adopts theseminal model of interdependent networks proposed by Buldyrev et al., in whichnew link failures occur in a network if the connectivity is lost in the pairednetwork. The problem of finding critical nodes is NP-hard; thus the aim of theapproach is to accurately solve the problem in feasible time for moderate-sizeproblem instances. The proposed approach consists of two phases. In the firstphase, the maximum number of failure propagation stages is computed byrepeatedly solving the Boolean satisfiability problem. This number is then usedin the second phase, where the set of critical nodes is computed using integerlinear programming. The results of applying this approach to a variety ofproblem instances demonstrate that the approach is feasible for up to at least30 nodes and can be used as the baseline to compare the performance ofheuristic solutions.

Finding Critical Nodes in Interdependent Networks with SAT and ILP Solvers