Network augmentation for disaster-resilience against geographically correlated failure

We introduce a formal framework for the study of augmenting networks in the plane for disaster-resilience, where a disaster is modeled by a straight-line segment. We generalize various graph structures from classical 2-edge-connectivity, including minimal cuts and blocks. The key concept that we introduce is that of an l-leaf, which builds on the fundamental "leaf-block " concept from classical augmentation. We present a number of algorithms for constructing the above-mentioned graph structures, including a sweep-line algorithm that finds all edge-cuts that can be destroyed by a single disaster. We also present an algorithm which optimally adds a single edge between a pair of l-leaves or blocks while avoiding certain disaster regions. Finally, we present a number of heuristic schemes for solving the disaster-resilient network augmentation problem and perform extensive experiments to demonstrate the power of the l-leaf concept within heuristic design.