Network vulnerability assessment under cascading failures

Yilin Shen, My T. Thai

Abstract: The assessment of network vulnerability is of great importance in the presence of unexpected disruptive events or adversarial attacks, which will lead to a much more devastating consequence especially when failures can be cascaded. In this context, we study the Cascading Vulnerability Node Detection (CVND) optimization problem to identify the most vulnerable nodes in a network whose removals maximally destroy the network's functions after cascading failures, based on the recently proposed effective metric, total pairwise connectivity. Besides its NP-hardness on various graphs, we further show that the CVND problem is NP-hard to be approximated within Ω ((1+(d/n1-∈ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sub> ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (n-k)/n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∈</sup> )) equation with n vertices and k vulnerable nodes after d-hop failure cascades. Despite the intractability of this problem, we propose TRGA, a novel iterative two-phase algorithm, for efficiently solving the CVND problem in a timely manner. We also formulate the integer linear programming for obtaining the optimal solution. The effectiveness of our solutions is validated on various synthetic and real-world networks.