Identifying critical nodes in undirected graphs: Complexity results and polynomial algorithms for the case of bounded treewidth

Addis, Bernardetta; Summa, Marco Di; Grosso, Andrea

doi:10.1016/j.dam.2013.03.021

Cited by 69 publications

(87 citation statements)

References 25 publications

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“…The time complexity of finding out all-pairs shortest paths is O(|V| 3 ). An influenced set of any given node can be identified by checking O(|V|) nodes, the algorithm takes O(|V| 2 ) to find influenced sets for all the nodes in the network.…”

Section: B Time Complexity Analysismentioning

confidence: 99%

“…We select v 3 , v 4 and v 6 as critical nodes highlighted in blue, v 3 can support v 1 , v 2 and v 3 , v 4 can support v 2 , v 4 and v 5 , v 6 can support v 2 and v 6 . All nodes' requirements have been satisfied.…”

Section: A Examplementioning

confidence: 99%

“…Yew-Yih Cheng et al [2] propose a new centrality measures called DelayFlow to determine critical nodes in a transportation network so as to improve the design of the network as well as to devise plans for coping with network failures. Bernardetta Addis et al [3] consider the problem of deleting a limited number of nodes from a graph in order to minimize a connectivity measure of the surviving nodes. Dung T. Nguyen et al [4] study the Interdependent Power Network Disruptor (IPND) optimization problem to identify critical nodes in an interdependent power network whose removals maximally destroy its functions due to both malfunction of these nodes and the cascading failures of its interdependent communication network.…”

Section: Related Workmentioning

confidence: 99%

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A novel critical node in generalized networking

Zhou

2014

2014 20th International Conference on Automation and Computing

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Critical Nodes problem is an important problem in networking. There are several types of critical nodes which having been defined. In this paper, we propose a novel type of critical nodes based on two important parameters: range and support. How to find the critical nodes to make the networking stable is the key problem. We prove that the decision form of this problem (the total cost is no more than a given threshold) is NP-complete and the optimization form of this problem (to obtain the minimum total cost) is NP-hard. Then we bring out a heuristic algorithm to solve this problem and apply this problem to banking ATM placement problem. Finally, we analyse the advantages of our heuristic algorithm.

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Section: B Time Complexity Analysismentioning

confidence: 99%

Section: A Examplementioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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A novel critical node in generalized networking

Zhou

2014

2014 20th International Conference on Automation and Computing

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“…The minimum vertex/edge blocker and the most vital vertices/ edges problems have been studied in literature with respect to different graph properties, such as connectivity (Addis, Di Summa, & Grosso, 2013;Arulselvan, Commander, Elefteriadou, & Pardalos, 2009;Di Summa, Grosso, & Locatelli, 2011;Shen, Smith, & Goli, 2012;Veremyev, Prokopyev, & Pasiliao, 2014), shortest path (Bar-Noy et al, 1995;Israeli & Wood, 2002;Khachiyan et al 2008), maximum flow (Altner, Ergun, & Uhan, 2010;Ghare, Montgomery, & Turner, 1971;Wollmer, 1964;Wood, 1993), spanning tree (Bazgan, Toubaline, & Vanderpooten, 2012;2013;Frederickson & Solis-Oba, 1996), assignment (Bazgan, Toubaline, & Vanderpooten, 2010b), 1-median (Bazgan et al, 2010a), 1-center (Bazgan et al, 2010a), matching (Ries et al, 2010;Zenklusen, 2010;Zenklusen et al, 2009), independent sets (Bazgan et al, 2011), vertex covers (Bazgan et al, 2011), andcliques (Mahdavi Pajouh, Boginski, &.…”

Section: Previous Work and Our Contributionsmentioning

confidence: 99%

Minimum edge blocker dominating set problem

Pajouh

Walteros

Boginski

et al. 2015

European Journal of Operational Research

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“…Relatively few exact and heuristic methods have been proposed for the critical node detection problem (Borgatti 2006;Dinh et al 2010Dinh et al , 2012Summa et al 2011Summa et al , 2012Shen et al 2013;Addis et al 2013) and most have addressed small or special graphs (e.g. trees).…”

Section: Introductionmentioning

confidence: 99%

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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Identifying critical nodes in undirected graphs: Complexity results and polynomial algorithms for the case of bounded treewidth

Cited by 69 publications

References 25 publications

A novel critical node in generalized networking

A novel critical node in generalized networking

Minimum edge blocker dominating set problem

Heuristic identification of critical nodes in sparse real-world graphs

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