On Network Topology Augmentation for Global Connectivity under Regional Failures

Abstract

Several recent studies shed light on the vulnerability of networks against regional failures, which are failures of multiple nodes and links in a physical region due to a natural disaster. The paper defines a novel design framework, called Geometric Network Augmentation (GNA), which determines a set of node pairs and the new cable routes to be deployed between each of them to make the network always remain connected when a regional failure of a given size occurs. With the proposed GNA design framework, we provide mathematical analysis and efficient heuristic algorithms that are built on the latest computational geometry tools and combinatorial optimization techniques. Through extensive simulation we show that augmentation with just a small number of new cable routes will achieve the desired resilience against all the considered regional failures.

The complexity landscape of disaster‐aware network extension problems

“…Throughout Sections 2 and 3, we focus on worst-case analysis. In papers considering worst-case problems [2,3,25,28], the network is modeled as an undirected connected geometric graph G = (V, E) with n = |V | nodes and m = |E| edges. The nodes are embedded as points in the Euclidean plane.…”

“…Proposition 1 (Claim 4 of [25]). We are given a connected Planar Graph G = (V, E) with links considered as polygonal chains, a uniform cable cost function, a radius r, a single danger zone Z and two nodes s, t of G. Finding a minimum cost edge between the given nodes with maximal protection for danger zone Z can always be done in polynomial time.…”

“…The edge is along a predefined grid, where it can take a vertical, horizontal, or diagonal line segment. The dotted (green) curve demonstrates the shape of the added cables in a worst-case model (like the model of [25]). There, it avoids a circular area to survive disk failures.…”

“…Throughout Sections 2 and 3, we focus on worst‐case analysis. In papers considering worst‐case problems [2, 3, 25, 28], the network is modeled as an undirected connected geometric graph $$$ \mathcal{G}=\left(\mathcal{V},\mathcal{E}\right) $$$ with $$$ n=\mid \mathcal{V}\kern0.2em \mid $$$ nodes and $$$ m=\mid \mathcal{E}\mid $$$ edges. The nodes are embedded as points in the Euclidean plane.…”

“…We would like to highlight that this article is an extended and thoroughly revised version of our conference paper [28]. In the original study, we put more emphasis on comparing the results of two recent papers [22,25] and investigating the complexities of the problems tackled by them. The current paper has a larger scope, summarizing and charting the complexity results of related prior works (see Tables 1 and 2).…”