Branch and cut algorithms for detecting critical nodes in undirected graphs

Summa, Marco Di; Grosso, Andrea; Locatelli, Marco

doi:10.1007/s10589-012-9458-y

Cited by 95 publications

(56 citation statements)

References 19 publications

(31 reference statements)

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“…A general mathematical formulation of this problem is how to select a subset of nodes in a graph so that after the removal of selected nodes, the connectivity of the rest of the graph is minimized, which is known as NPhard [22]. Heuristics and algorithms have been to proposed to solve this problem by putting certain constraints on the types of graph structure [22]- [24]. However, these solutions cannot be applied to general weighted graphs.…”

Section: Background and Related Workmentioning

confidence: 99%

Analysis of critical node attacks in mobile ad hoc networks

Zhang

Sterbenz

2014

2014 6th International Workshop on Reliable Networks Design and Modeling (RNDM)

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Understanding network behavior under challenges is essential to constructing a resilient and survivable network. Due to the mobility and wireless channel properties, it is more difficult to model and analyze MANETs (mobile ad hoc networks) under various challenges. Previously, we have modeled network attacks based on a priori complete knowledge of network structure and mobility. In this paper, we present the analysis of MANET behavior under random node failures and centralitybased attacks based on real-time topological information, and provide a comparison of network performance under complete information and real-time attacks. In addition, we adapt betweenness and closeness centrality to measure node significance in asymmetric source/sink network scenarios. The ns-3 simulator is used to examine network throughput under various intelligent attacks. By analyzing network topological properties, we provide a theoretical verification of the simulation results.Index Terms-mobile wireless topology challenge modeling, MANET, time-varying weighted graph, resilient survivable disruption-tolerant network, ns-3 simulation 978-1-4799-7040-7 ©2014 IEEE

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Section: Background and Related Workmentioning

confidence: 99%

Analysis of critical node attacks in mobile ad hoc networks

Zhang

Sterbenz

2014

2014 6th International Workshop on Reliable Networks Design and Modeling (RNDM)

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“…Jose C. Nacher [6] investigate the role of nodes when a minimum dominating set (MDS) approach is considered in controlling a network, and present an algorithmic procedure to compute the critical and redundant nodes using the MDS. Marco Di Summa et al [10] deal with another type of critical node problem, where a given number of nodes has to be removed from an undirected graph in order to maximize the disconnections between the node pairs of the graph.…”

Section: Related Workmentioning

confidence: 99%

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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“…Identifying important nodes in a network is a rich area of research (see [3,18,[34][35][36][37][38][39][40] for a sample of literature on the topic) with a variety of related applications, for example, marketing [17], communication [42], security [11], or social network analysis [7]. Critical node detection problems (CNP) in networks are used to ascertain the strongest (weakest) nodes of a network according to various connectivity-based metrics [41] detailed later in this paper.…”

Section: Introductionmentioning

confidence: 99%

“…To ensure optimality, we turn to exact algorithms [3,41,42] and exploit integer programming methods to achieve a truly optimal solution given a suitable metric as an objective function. Other algorithms for CNP are explored in [2,18,36] for specific classes of networks (e.g. sparse networks).…”

Section: Introductionmentioning

confidence: 99%

Robustness of solutions to critical node detection problems with imperfect data: a computational study

Gillen

Veremyev

Prokopyev

et al. 2016

Optimization Methods and Software

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A class of critical node detection problems based upon the metric of communication efficiency is considered. While both exact integer programming and heuristic centrality-based methods exist for the solution of these problems, previous work has been mostly focused on the case where perfect information about the network is available. In this paper we suppose that some level of misinformation about nodes or edges has been inflicted on the observer's perception of the network, that is, there are hidden elements or fake additional elements. An extensive computational study is conducted to ascertain whether the exact integer-programming-based solutions perform better under imperfect information than heuristic methods. For large networks, exact methods cannot produce a solution in a reasonable amount of time, hence an approximation of the exact method is also considered for such instances. The obtained approximate solutions are again compared to centrality-based heuristics under the presence of imperfect data.

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Branch and cut algorithms for detecting critical nodes in undirected graphs

Cited by 95 publications

References 19 publications

Analysis of critical node attacks in mobile ad hoc networks

Analysis of critical node attacks in mobile ad hoc networks

A novel critical node in generalized networking

Robustness of solutions to critical node detection problems with imperfect data: a computational study

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