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We study the robustness of interdependent networks, in which the state of one network depends on the state of the other network and vice versa. In particular, we focus on the interdependency between the power grid and communication networks, where the grid depends on communications for its control, and the communication network depends on the grid for power. A real-world example is the Italian blackout of 2003, when a small failure in the power grid cascaded between the two networks and led to a massive blackout. In this paper, we study the minimum number of node failures needed to cause total blackout (i.e., all nodes in both networks to fail). In the case of unidirectional interdependency between the networks we show that the problem is NP-hard, and develop heuristics to find a near-optimal solution. On the other hand, we show that in the case of bidirectional interdependency this problem can be solved in polynomial time. We believe that this new interdependency model gives rise to important, yet unexplored, robust network design problems for interdependent networked infrastructures.

Robustness of interdependent networks: The case of communication networks and the power grid