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Heuristic identification of critical nodes in sparse real-world graphs

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Abstract

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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  1. dmclique, ftp://dimacs.rutgers.edu in directory /pub/dsj/clique

References

  • Addis, B., Di Summa, M., Grosso, A.: Identifying critical nodes in undirected graphs: complexity results and polynomial algorithms for the case of bounded tree width. Discret. Appl. Math. 161(16), 2349–2360 (2013)

    Article  MATH  Google Scholar 

  • Arulselvan, A., Commander, C.W., Pardolas, P.M., Shylo, O.: Managing network risk via critical node identification. In: Gülpinar, N., Rüstem, B. (eds.) Risk Management in Communications Systems. Springer-Verlag, Hiedelburg (2009)

    Google Scholar 

  • Arulselvan, A., Commander, C., Shylo, O., Pardolas, P.: Cardinality-constrained critical node detection problem. In: Gülpinar, N., Harrison, P., Rüstem, B. (eds.) Performance Models and Risk Management in Communications Systems, pp. 79–91. Springer-Verlag, Hiedelburg (2011)

    Chapter  Google Scholar 

  • Arulselvan, A., Commander, C.W., Elefteriadou, L., Pardolas, P.M.: Detecting critical nodes in sparse graphs. Comput. Oper. Res. 36, 2193–2200 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • Boginski, V., Commander, C.W.: Identifying critical nodes in protein-protein interaction networks. In: Butenko, S., Chaovilitwongse, W.A., Pardalos, P.M. (eds.) Clustering Challenges in Biological Networks, pp. 153–166. World Scientific Publishing Co., New Jersey, USA (2008)

  • Borgatti, S.P.: Identifying sets of key players in a social network. Comput. Math. Organ. Theory 12(1), 21–34 (2006)

    Article  MATH  Google Scholar 

  • Davis, T.A., Hu, Y.: The university of florida sparse matrix collection. ACM Trans. Math. Softw. 38, 1–25, http://www.cise.ufl.edu/research/sparse/matrices/ (2011)

  • Di Summa, M., Grosso, A., Locatelli, M.: Complexity of the critical node problem over trees. Comput. Oper. Res. 38(12), 1766–1774 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • Di Summa, M., Grosso, A., Locatelli, M.: Branch and cut algorithms for detecting critical nodes in undirected graphs. Comput. Optim. Appl. 53(3), 649–680 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Dinh, T., Xuan, Y., Thai, M., Park, E., Znati, T.: On approximation of new optimisation methods for assessing network vulnerability. In: INFOCOM, 2000 Proceedings of the IEEE, pp. 1–9 (2010)

  • Dinh, T., Xuan, Y., Thai, M., Pardalos, P., Znati, T.: On new approaches of assessing network vulnerability: hardness and approximation. IEEE/ACM Trans. Netw. 20(2), 609–619 (2012)

    Article  Google Scholar 

  • Dinh, T., Thai, M.T., Nguyen, H.T.: Bound and exact methods for assessing link vulnerability in complex networks. J Comb. Optim. 28(1), 3–24 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  • Edalatmanesh, M.: Heuristics for the critical node detection problem in large complex networks. Brock University, St. Catharines, Ontario, vol. 6, http://www.dr.library.brocku.ca/bitstream/handle/10464/4984/Brock_Edalatmanesh_Mahmood_2013.pdf?sequence=1 (2013)

  • Fan, N., Pardalos, P.M.: Robust optimisation of graph partitioning and critical node detection in analysing networks, In: Wu, W., Daescu, O. (eds.) Combinatorial Optimization and Applications, vol. 6508 of Lecture notes in computer science, pp. 170–183. Springer, Berlin (2010)

  • Krebs, V.: Uncloaking terrorist networks, http://www.firstmonday.org/issues/issue7_4/krebs/ (2002)

  • Medlock, J., Galvani, A.P.: Optimizing influenza vaccine distribution. Science 325, 1705–1708 (2009)

    Article  Google Scholar 

  • Nguyen, D.T., Shen, M.T., Thai, M.T.: Detecting critical nodes in interdependent power networks for vulnerability assessment. IEEE Trans. Smart Grid 99, 1–9 (2013)

    Google Scholar 

  • Shen, Y., Dinh, T.N., Thai, M.T.: Adaptive algorithms for detecting critical links and nodes in dynamic networks. In: Proceedings of the IEEE Military Communications Conference–MILCOM (2012)

  • Shen, Y., Nguyen, N.P., Xuan, Y., Thai, M.T.: On the discovery of critical links and nodes for assessing network vulnerability. IEEE/ACM Trans. Netw. 21(3), 963–973 (2013)

    Article  Google Scholar 

  • Sun, F., Shayman, M.A.: On pairwise connectivity of wireless multi hop networks. Int. J. Secur. Netw. 2(1/2), 37–49 (2007)

    Article  Google Scholar 

  • Ventresca, M., Aleman, D.: A fast greedy algorithm for the critical node detection problem. In: Zhang, Z., Wu, L., Xu, W., Du, D.-Z. (eds.) Combinatorial Optimisation and Applications, vol. 8851 of Lecture notes in computer science, pp. 613–624. Springer (2014)

  • Ventresca, M., Aleman, D.: A region growing algorithm for detecting critical nodes. In: Zhang, Z., Wu, L., Xu, W., Du, D.Z. (eds.) Combinatorial Optimisation and Applications, vol. 8851 of Lecture notes in computer science, pp. 593–612. Springer (2014)

  • Ventresca, M., Aleman, D.: Approximation algorithms for detecting critical nodes, In: NATO Science for Peace and Security Series-D: Information and Communication Security, pp. 289–305, IOS Press (2014)

  • Ventresca, M.: Global search algorithms using a combinatorial unranking-based problem representation for the critical node detection problem. Comput. Oper. Res. 39, 2763–2775 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Ventresca, M., Aleman, D.: A derandomized approximation algorithm for the critical node detection problem. Comput. Oper. Res. 43, 261–270 (2014)

    Article  MathSciNet  Google Scholar 

  • Veremyev, A., Boginski, V., Pasiliao, E.L.: Exact identification of critical nodes in sparse networks via new compact formulations. Optim. Lett. 8(1), 1245–1259 (2014)

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Acknowledgments

The author would like to thank Andrea Grosso, Dipartimento di Informatica, Università degli Studi di Torino, for discussions on the critical node detection problem. In addition the author would like to thank the anonymous referees whose questions and suggestions resulted in a considerable improvement in this paper.

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Correspondence to Wayne Pullan.

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Pullan, W. Heuristic identification of critical nodes in sparse real-world graphs. J Heuristics 21, 577–598 (2015). https://doi.org/10.1007/s10732-015-9290-5

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