Finding Critical Regions and Region-Disjoint Paths in a Network

Abstract

Abstract-Due to their importance to society, communication networks should be built and operated to withstand failures. However, cost considerations make network providers less inclined to take robustness measures against failures that are unlikely to manifest, like several failures coinciding simultaneously in different geographic regions of their network.Considering networks embedded in a two-dimensional plane, we study the problem of finding a critical region -a part of the network that can be enclosed by a given elementary figure of predetermined size -whose destruction would lead to the highest network disruption. We determine that only a polynomial, in the input, number of non-trivial positions for such a figure need to be considered and propose a corresponding polynomialtime algorithm. In addition, we consider region-aware network augmentation to decrease the impact of a regional failure. We subsequently address the region-disjoint paths problem, which asks for two paths with minimum total weight between a source (s) and a destination (d) that cannot both be cut by a single regional failure of diameter D (unless that failure includes s or d). We prove that deciding whether region-disjoint paths exist is NP-hard and propose a heuristic region-disjoint paths algorithm.

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

“…Understanding how to deal with circular disk failures is a good start; however, one should consider other disaster shapes too. In , it is proven that, in a similar problem setting (the model of considers that a link is hit by a disaster exactly if at least one of its endpoints is inside the disaster region. We believe our failure model is more realistic), there are a polynomial number of maximal failures caused by disasters having elliptic or polygonal (e.g., rectangular or equilateral triangular) shape.…”

A survey of strategies for communication networks to protect against large-scale natural disasters

“…By using a slightly relaxed failure model in which only links that have at least one endpoint in the failure region are destroyed, Trajanovski et al [16] are able to determine the most vulnerable region for a failure of circular shape at a reduced complexity than that of [15]. Moreover, they can exactly and in polynomial time determine such vulnerable regions also for failures of elliptical shape and for shapes represented by a polygon.…”

“…Trajanovski et al [16] address the problem of finding two region-disjoint paths that (with the exception of the regions around the source and destination) cannot both be cut by a failure of given diameter. In this case, the shape of the failing region is not important, only its diameter is (as it could be rotated in any direction).…”

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“…In many prior works, the objective is to find the most vulnerable network area of a predefined size, under specific disaster models, e.g., under line disasters [8], circular disasters [8], [9], or general polygon disasters [10]. For all the network components that intersect the disaster, they 50 may become definitely inoperative [5], [8] or fail with a probability [9], [11].…”