The healing strategy by prioritizing minimum degree against localized attacks on interdependent spatially embedded networks

Abstract

Many real infrastructure networks, such as power grids and communication networks, are not only depend on one another to function, but also embedded in space. A lot of works have been devoted to reveal the vulnerability of interdependent spatially embedded networks considers random failures. However, recently research show that they are susceptible to geographically localized attacks or failures cased by natural disasters or terrorist attacks, which affect all nodes within a given radius. In particular, small localized attacks may lead to catastrophic consequences. As a remedy of the collapse instability, one research introduced a dynamic healing strategy and the possibility of new connectivity link with a probability, called random healing, to bridge two remaining neighbors of a failed node. The random strategy is straightforward. Here, unlike previous strategy, we propose a simple but effective strategy, called healing strategy by prioritizing minimum degree(HPMD), which establishing a new link between two functioning neighbors with minimum degree during the cascading failures. In addition, we consider the distance between two nodes to avoid change the network structures. Afterwards, a comparison is made between HPMD and three healing strategies: random, degree centrality and local centrality to identify which a pair of neighbors have high priority. Simulation experiments are presented for two square lattices with the same size as interdependent spatially embedded networks under localized attacks. Results demonstrated that HPMD strategy has an outstanding performance against localized attacks, even when ratio of healing is vary. Moreover, HPMD is more timely, more applicability and costless. Our method is meaningful in practice as it can greatly enhance the resilience and robustness of interdependent spatially embedded networks against localized attacks.