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International Conference on Combinatorial Optimization and Applications

COCOA 2014: Combinatorial Optimization and Applications pp 603–612Cite as

A Fast Greedy Algorithm for the Critical Node Detection Problem

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8881))

Abstract

The critical node detection problem (CNDP) aims to fragment a graph \(G=(V,E)\) by removing a set of vertices \(R\) with cardinality \(|R|\le K\) such that the residual graph has minimum pairwise connectivity. Algorithms that are capable of finding \(R\) in graphs with many thousands or millions of vertices are needed since existing approaches require significant computational cost and subsequently are useful for only very small network instances. An efficient method for evaluating the impact of removing any \(v \in V\) on the CNDP objective function within reasonable time and space complexity is then necessary. In this paper we propose a depth-first search solution to this problem that requires \(\mathcal {O}(|V|+|E|)\) complexity, and employ the method in a greedy algorithm for quickly identifying \(R\) in large networks. We evaluate the results using six real-world benchmark problems. The proposed algorithm can be easily extended to vertex and edge-weighted variants of the critical vertex detection problem.

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Author information

Authors and Affiliations

  1. School of Industrial Engineering, Purdue University, West Lafayette, USA

    Mario Ventresca

  2. Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Canada

    Dionne Aleman

Authors
  1. Mario Ventresca
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  2. Dionne Aleman
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Correspondence to Mario Ventresca .

Editor information

Editors and Affiliations

  1. Zhejiang Normal University, Jinhua, Zhejiang, China

    Zhao Zhang

  2. University of Texas, Tyler, Texas, USA

    Lidong Wu

  3. University of Texas, Dallas, Texas, USA

    Wen Xu

  4. University of Texas, Dallas, USA

    Ding-Zhu Du

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© 2014 Springer International Publishing Switzerland

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Ventresca, M., Aleman, D. (2014). A Fast Greedy Algorithm for the Critical Node Detection Problem. In: Zhang, Z., Wu, L., Xu, W., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2014. Lecture Notes in Computer Science(), vol 8881. Springer, Cham. https://doi.org/10.1007/978-3-319-12691-3_45

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  • DOI: https://doi.org/10.1007/978-3-319-12691-3_45

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12690-6

  • Online ISBN: 978-3-319-12691-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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