The Effective Healing Strategy against Localized Attacks on Interdependent Spatially Embedded Networks

Many real-world infrastructure networks, such as power grids and communication networks, always depend on each other by their functional components that share geographic proximity. A lot of works were devoted to revealing the vulnerability of interdependent spatially embedded networks (ISENs) when facing node failures and showed that the ISENs are susceptible to geographically localized attacks caused by natural disasters or terrorist attacks. How to take emergency methods to prevent large scale of cascading failures on interdependent infrastructures is a longstanding problem. Here, we propose an effective strategy for the healing of local structures using the connection profile of a failed node, called the healing strategy by prioritizing minimum degrees (HPMD), in which a new link between two active low-degree neighbors of a failed node is established during the cascading process. Afterwards, comparisons are made between HPMD and three healing strategies based on three metrics: random choice, degree centrality, and local centrality, respectively. Simulations are performed on the ISENs composed of two diluted square lattices with the same size under localized attacks. Results show that HPMD can significantly improve the robustness of the system by enhancing the connectivity of low-degree nodes, which prevent the diffusion of failures from low-degree nodes to moderate-degree nodes. In particular, HPMD can outperform other three strategies in the size of the giant component of networks, critical attack radius, and the number of iterative cascade steps for a given quota of newly added links, which means HPMD is more effective, more timely, and less costly. The high performance of HPMD indicates low-degree nodes should be placed on the top priority for effective healing to resist the cascading of failures in the ISENs, which is totally different from the traditional methods that usually take high-degree nodes as critical nodes in a single network. Furthermore, HPMD considers the distance between a pair of nodes to control the variation in the network structures, which is more applicable to spatial networks than previous methods