Robustness of Bidirectional Interdependent Networks: Analysis and Design

We study the robustness of interdependent networks where two networks are said to be interdependent if the operation of one network depends on the operation of the other one, and vice versa. In this paper, we propose a model for analyzing bidirectional interdependent networks with known topology. We define the metric MR(D) to be the minimum number of nodes that should be removed from one network to cause the failure of D nodes in the other network due to cascading failures. We prove that evaluating this metric is not only NP-complete, but also inapproximable. Next, we propose heuristics for evaluating this metric and compare their performances using simulation results. Finally, we introduce two closely related definitions for robust design of interdependent networks; propose algorithms for explicit design, and demonstrate the relation between robust interdependent networks and expander graphs.