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Many real infrastructure networks, such as power grids and communicationnetworks, are not only depend on one another to function, but also embedded inspace. A lot of works have been devoted to reveal the vulnerability ofinterdependent spatially embedded networks considers random failures. However,recently research show that they are susceptible to geographically localizedattacks or failures cased by natural disasters or terrorist attacks, whichaffect all nodes within a given radius. In particular, small localized attacksmay lead to catastrophic consequences. As a remedy of the collapse instability,one research introduced a dynamic healing strategy and the possibility of newconnectivity link with a probability, called random healing, to bridge tworemaining 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), whichestablishing a new link between two functioning neighbors with minimum degreeduring the cascading failures. In addition, we consider the distance betweentwo nodes to avoid change the network structures. Afterwards, a comparison ismade between HPMD and three healing strategies: random, degree centrality andlocal centrality to identify which a pair of neighbors have high priority.Simulation experiments are presented for two square lattices with the same sizeas interdependent spatially embedded networks under localized attacks. Resultsdemonstrated that HPMD strategy has an outstanding performance againstlocalized attacks, even when ratio of healing is vary. Moreover, HPMD is moretimely, more applicability and costless. Our method is meaningful in practiceas it can greatly enhance the resilience and robustness of interdependentspatially embedded networks against localized attacks.

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