Exact identification of critical nodes in sparse networks via new compact formulations

Veremyev, Alexander; Boginski, Vladimir; Pasiliao, Eduardo L.

doi:10.1007/s11590-013-0666-x

Cited by 85 publications

(65 citation statements)

References 16 publications

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“…See, for instance, Shen et al (2012), Granata et al (2013), Veremyev, Boginski and Pasiliao (2014), Veremyev, Prokopyev and Pasiliao (2014), a survey in Walteros and Pardalos (2012) and the references given therein.…”

Section: Introductionmentioning

confidence: 99%

Sequential Shortest Path Interdiction with Incomplete Information

2016

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We study sequential interdiction when the interdictor has incomplete initial information about the network, and the evader has complete knowledge of the network, including its structure and arc costs. In each time period, the interdictor blocks at most k arcs from the network observed up to that period, after which the evader travels along a shortest path between two (fixed) nodes in the interdicted network. By observing the evader's actions, the interdictor learns about the network structure and arc costs, and adjusts its actions so as to maximize the cumulative cost incurred by the evader. A salient feature of our work is that the feedback in each period is deterministic and adversarial. In addition to studying the regret minimization problem, we also discuss time-stability of a policy, which is the number of time periods until the interdictor's actions match those of an oracle interdictor with prior knowledge of the network. We propose a class of simple interdiction policies that have a finite regret and detect when the instantaneous regret reaches zero in real time. More importantly, we establish that this class of policies belongs to the set of efficient policies.

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Section: Introductionmentioning

confidence: 99%

Sequential Shortest Path Interdiction with Incomplete Information

2016

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“…The problem can be defined either by upper-bounding the number of critical nodes and maximizing the degradation metric, or by lowerbounding the degradation metric and minimizing the number of critical nodes. Veremyev et al [8] address two CND variants defined on a simple undirected graph G. In the first variant, for a given integer K, the aim is to identify a set of K critical nodes minimizing the pairwise connectivity (also referred to as the average 2-terminal reliability metric in other works). In the second variant, for a given integer L, the aim is to identify a minimum set of critical nodes, so that the largest connected component in the remaining graph contains no more than L nodes.…”

Section: A Measures Of Network Vulnerabilitymentioning

confidence: 99%

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

Gomes

Tapolcai

Esposito

et al. 2016

2016 8th International Workshop on Resilient Networks Design and Modeling (RNDM)

110

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Abstract-Recent natural disasters have revealed that emergency networks presently cannot disseminate the necessary disaster information, making it difficult to deploy and coordinate relief operations. These disasters have reinforced the knowledge that telecommunication networks constitute a critical infrastructure of our society, and the urgency in establishing protection mechanisms against disaster-based disruptions.Hence, it is important to have emergency networks able to maintain sustainable communication in disaster areas. Moreover, the network architecture should be designed so that network connectivity is maintained among nodes outside of the impacted area, while ensuring that services for costumers not in the affected area suffer minimal impact.As a first step towards achieving disaster resilience, the RE-CODIS project was formed, and its Working Group 1 members conducted a comprehensive literature survey on "strategies for communication networks to protect against large-scale natural disasters," which is summarized in this article.Index Terms-vulnerability, end-to-end resilience, natural disasters, disaster-based disruptions.

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“…The metric to be minimised for CNP1 is the percentage . The metric to be minimised for CNP2 is C 2 = |S|, the number of nodes removed from G. This variant is referred to as the cardinality constrained critical node detection problem and was first proposed in Arulselvan et al (2011) Linear 0-1 versions of these two problems have been formulated (Veremyev et al 2014) using the following definitions:…”

Section: Introductionmentioning

confidence: 99%

“…In Veremyev et al (2014) it was observed that all available exact methods for solving critical node problems for the general case of an undirected graph deal with the linear 0-1 formulations listed in Eqs. 1-10 included the O(n 3 ) triangular connectivity constraints (Eqs.…”

Section: Introductionmentioning

confidence: 99%

“…These two solution methods were able to find exact solutions for real-world sparse networks up to 10 times larger and with CPU time up to 1000 times faster when compared to previous studies. All graphs used in Veremyev et al (2014) were obtained from the University of Florida Sparse Matrix Collection (Davis and Hu 2011) and their exact method was able to solve the CNP1/CNP2 problems for graphs with up to 1138 nodes. It should be noted that graphs of this size are still difficult for state of the art heuristic CNP algorithms to solve.…”

Section: Introductionmentioning

confidence: 99%

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Heuristic identification of critical nodes in sparse real-world graphs

Pullan

2015

J Heuristics

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Given a graph, the critical node detection problem can be broadly defined as identifying the minimum subset of nodes such that, if these nodes were removed, some metric of graph connectivity is minimised. In this paper, two variants of the critical node detection problem are addressed. Firstly, the basic critical node detection problem where, given the maximum number of nodes that can be removed, the objective is to minimise the total number of connected nodes in the graph. Secondly, the cardinality constrained critical node detection problem where, given the maximum allowed connected graph component size, the objective is to minimise the number of nodes required to be removed to achieve this. Extensive computational experiments, using a range of sparse real-world graphs, and a comparison with previous exact results demonstrate the effectiveness of the proposed algorithms.

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Exact identification of critical nodes in sparse networks via new compact formulations

Cited by 85 publications

References 16 publications

Sequential Shortest Path Interdiction with Incomplete Information

Sequential Shortest Path Interdiction with Incomplete Information

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

Heuristic identification of critical nodes in sparse real-world graphs

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