The Earth is nearly flat: Precise and approximate algorithms for detecting vulnerable regions of networks in the plane and on the sphere

Several recent works shed light on the vulnerability of networks against regional failures, which are failures of multiple pieces of equipment in a geographical region as a result of a natural disaster. To enhance the preparedness of a given network to natural disasters, regional failures and associated Shared Risk Link Groups (SRLGs) should be first identified. For simplicity, most of the previous works assume the network is embedded on a Euclidean plane. Nevertheless, they are on the Earth's surface; this assumption causes distortion. In this work, we generalize some of the related results on the plane to the sphere. In particular, we focus on algorithms for listing SRLGs as a result of regional failures of circular or other fixed shape.