Geographic max-flow and min-cut under a circular disk failure model

Failures in fiber-optic networks may be caused by natural disasters, such as floods or earthquakes, as well as other events, such as an Electromagnetic Pulse (EMP) attack. These events occur in specific geographical locations, therefore the geography of the network determines the effect of failure events on the network's connectivity and capacity. In this paper we consider a generalization of the min-cut and max-flow problems under a geographic failure model. Specifically, we consider the problem of finding the minimum number of failures, modeled as circular disks, to disconnect a pair of nodes and the maximum number of failure disjoint paths between pairs of nodes. This model applies to the scenario where an adversary is attacking the network multiple times with intention to reduce its connectivity. We present a polynomial time algorithm to solve the geographic min-cut problem and develop an ILP formulation, an exact algorithm, and a heuristic algorithm for the geographic max-flow problem.National Science Foundation (U.S.) (Grant CNS-0830961)National Science Foundation (U.S.) (Grant CNS-1017714)National Science Foundation (U.S.) (Grant CNS-1017800)National Science Foundation (U.S.) (CAREER Grant 0348000)United States. Defense Threat Reduction Agency (Grant HDTRA1-07-1-0004)United States. Defense Threat Reduction Agency (Grant HDTRA-09-1-005

On the robustness of network infrastructures to disasters and physical attacks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 153-158).Networks are vulnerable to natural disasters, such as earthquakes or floods, as well as to physical attacks, such as an Electromagnetic Pulse (EMP) attack. Such realworld events happen in specific geographical locations and disrupt specific parts of the network. Therefore, the geographical layout of the network determines the impact of such events on the network's connectivity. We focus on network analysis and design under a geographic failure model of (geographical) networks to such disasters. Initially, we aim to identify the most vulnerable parts of data networks to attack. That is, the locations of a disaster that would have the maximum disruptive effect on a network in terms of capacity and connectivity. We consider graph models in which nodes and links are geographically located on a plane, and model the disaster event as a line segment or circular disk. We develop polynomial time algorithms for finding the worst possible cut in this setting. Then, we obtain numerical results for a specific backbone network, thereby demonstrating the applicability of our algorithms to real-world networks. We also develop tools to calculate network metrics after a 'random' geographic disaster. The random location of the disaster allows us to model situations where the physical failures are not targeted attacks. In particular, we consider disasters that take the form of a 'random' circular disk or line in a plane. Using results from geometric probability, we are able to calculate some network performance metrics to such a disaster in polynomial time. In particular, we can evaluate average two-terminal reliability in polynomial time under these 'random' cuts. This is in contrast to the case of independent link failures for which there exists no known polynomial time algorithm to calculate this reliability metric. We present some numerical results to show the significance of geometry on the survivability of the network. This motivates the formulation of several network design problems in the context of randomly located disasters. We also study some min-cut and max-flow problems in a geographical setting. Specifically, we consider the problem of finding the minimum number of failures, modeled as circular disks, to disconnect a pair of nodes and the maximum number of failure disjoint paths between a pair of nodes. This model applies to the scenario where an adversary is attacking the network multiple times with intention to reduce its connectivity. We present a polynomial time algorithm to solve the geographic mincut problem and develop an ILP formulation, an exact algorithm, and a heuristic algorithm for the geographic max-flow problem. Finally, we study the reliability of power transmission networks under regional disasters. Initially, we quantify the effect of large-scale non-targeted disasters and their resulting cascade effects on power networks. We then model the dependence of data networks on the power systems and consider network reliability in this dependent network setting. Our novel approach provides a promising new direction for modeling and designing networks to lessen the effects of geographical disasters or attacks.by Sebastian James Neumayer.Ph.D

Maximally spatial-disjoint lightpaths in optical networks

Lightpaths enable end-to-end all-optical transmission between network nodes. For survivable routing, traffic is often carried on a primary lightpath, and rerouted to another disjointed backup lightpath in case of the failure of the primary lightpath. Though both lightpaths can be physically disjointed, they can still fail simultaneously if a disaster affects them simultaneously on the physical plane. Hence, we propose a routing algorithm for provisioning a pair of link-disjoint lightpaths between two network nodes such that the minimum spatial distance between them (while disregarding safe regions) is maximized. Through means of simulation, we show that our algorithm can provide higher survivability against spatial-based simultaneous link failures (due to the maximized spatial distance)

Enhancing network robustness via shielding

We consider shielding critical links to guarantee network connectivity under geographical and general failure models. We develop a mixed integer linear program (MILP) to obtain the minimum cost shielding to guarantee the connectivity of a single SD pair under a general failure model, and exploit geometric properties to decompose the shielding problem under a geographical failure model. We extend our MILP formulation to guarantee the connectivity of the entire network, and use Benders decomposition to significantly reduce the running time by exploiting its partial separable structure. We also apply simulated annealing to solve larger network problems to obtain near-optimal solutions in much shorter time. Finally, we extend the algorithms to guarantee partial network connectivity, and observe significant reduction in shielding cost, especially when the failure region is small. For example, when the failure region radius is 60 miles, we observe as much as 75% reduction in shielding cost by relaxing the connectivity requirement to 95% on a major US infrastructure network

Most vital segment barriers

We study continuous analogues of "vitality" for discrete network flows/paths, and consider problems related to placing segment barriers that have highest impact on a flow/path in a polygonal domain. This extends the graph-theoretic notion of "most vital arcs" for flows/paths to geometric environments. We give hardness results and efficient algorithms for various versions of the problem, (almost) completely separating hard and polynomially-solvable cases

On critical service recovery after massive network failures

This paper addresses the problem of efficiently restoring sufficient resources in a communications network to support the demand of mission critical services after a large-scale disruption. We give a formulation of the problem as a mixed integer linear programming and show that it is NP-hard. We propose a polynomial time heuristic, called iterative split and prune (ISP) that decomposes the original problem recursively into smaller problems, until it determines the set of network components to be restored. ISP's decisions are guided by the use of a new notion of demand-based centrality of nodes. We performed extensive simulations by varying the topologies, the demand intensity, the number of critical services, and the disruption model. Compared with several greedy approaches, ISP performs better in terms of total cost of repaired components, and does not result in any demand loss. It performs very close to the optimal when the demand is low with respect to the supply network capacities, thanks to the ability of the algorithm to maximize sharing of repaired resources