Precise structural vulnerability assessment via mathematical programming

Network vulnerability assessment is an indispensable component of attack risk reduction and proactive response. However, traditional assessment methods simply assume the attacks only target at nodes with high degree or betweenness centrality, thus fail to capture the worst-case scenarios under simultaneous failures. In our previous work, we formulated assessing network vulnerability as optimization problems, so-called β-edge disruptor and β-vertex disruptor, to identify the minimum cost critical infrastructures that removal expose the network to a certain disruption level. Here, the disruption is measured as the fraction of node pairs with no paths between them in the residual network. In this paper, we present an exact analytical solution for the vulnerability assessment problems i.e. an exact branch-and-cut algorithm to solve the integer programming formulation of the β-vertex disruptor. The two intriguing aspects of the algorithms are an efficient Mixed Integer Programming (MIP) formulation, called sparse metric, and vertex-cut inequalities, a specialized cutting plane procedure that tightens the bound on the optimal solutions. Experiments on both synthetic and real-world networks suggest that our algorithm yields a significant improvement on a large variety of network instances, raising the size of the largest instance solved from several dozen to several hundred nodes. Our techniques can be easily extended to many graph partitioning and connectivity optimization problems.