Cascading failures are a critical vulnerability of complex information orinfrastructure networks. Here we investigate the properties of load-basedcascading failures in real and synthetic spatially-embedded network structures,and propose mitigation strategies to reduce the severity of damages caused bysuch failures. We introduce a stochastic method for optimal heterogeneousdistribution of resources (node capacities) subject to a fixed total cost.Additionally, we design and compare the performance of networks with N-stableand (N-1)-stable network-capacity allocations by triggering cascades usingvarious real-world node-attack and node-failure scenarios. We show that failuremitigation through increased node protection can be effectively achievedagainst single node failures. However, mitigating against multiple nodefailures is much more difficult due to the combinatorial increase in possiblefailures. We analyze the robustness of the system with increasing protection,and find that a critical tolerance exists at which the system undergoes a phasetransition, and above which the network almost completely survives an attack.Moreover, we show that cascade-size distributions measured in this regionexhibit a power-law decay. Finally, we find a strong correlation betweencascade sizes induced by individual nodes and sets of nodes. We also show thatnetwork topology alone is a weak factor in determining the progression ofcascading failures.
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