The critical node selection problem (CNP) has important applications in telecommunication, supply chain design, and disease propagation prevention. In practice, the weights on the connections are either uncertain or hard to estimate so recently robust optimization approaches have been considered for CNP. In this article, we address very general uncertainty sets, only requiring a linear optimization oracle. In particular, we can deal with interval uncertainty, scenario based uncertainty, Gamma-uncertainty, and ellipsoidal uncertainty. For this general class of robust critical node selection problems (RCNP), we propose an exact solution method based on Benders decomposition. The Benders subproblem, which in our approach is a robust optimization problem, is essentially solved by applying the Floyd-Warshall algorithm. The presented approach is tested on 832 instances based on random planar and Barabási-Albert graphs with different number of nodes and graph densities, where running times are compared to CPLEX being directly applied to the robust problem formulation. The computational results show the advantage of the proposed approach in handling the uncertainty thus outperforming CPLEX most notably for the ellipsoidal uncertainty cases.
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