Skip to main content
SpringerLink
Log in

Hardness and Approximation of Network Vulnerability

  • Reference work entry
  • First Online:
Handbook of Combinatorial Optimization

  • 7181 Accesses

Abstract

Assessing network vulnerability is a central research topic to understand networks structures, thus providing an efficient way to protect them from attacks and other disruptive events. Existing vulnerability assessments mainly focus on investigating the inhomogeneous properties of graph elements, node degree, for example; however, these measures and the corresponding heuristic solutions cannot either provide an accurate evaluation over general network topologies or performance guarantees to large-scale networks. To this end, this chapter introduces two new optimization models to quantify the network vulnerability, which aim to discover the set of key node/edge disruptors, whose removal results in the maximum decline of the global pairwise connectivity. Results presented in this chapter consist of the NP-completeness and inapproximability proofs of these problems along with pseudo-approximation algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 3,400.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 549.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Recommended Reading

  1. R. Albert, H. Jeong, A.-L. Barabasi, Error and attack tolerance of complex networks. Nature 406, 378–482 (2000)

    Article  Google Scholar 

  2. R. Ravi, D. Williamson, An approximation algorithm for minimum cost vertex connectivity problems, in Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms (ACM, New York, 1995), pp. 332–341

    Google Scholar 

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

    Article  MATH  Google Scholar 

  4. E. Zio, C.M. Rocco, D.E. Salazar, G. Muller, Complex Networks Vulnerability: a multiple-objective optimization approach, in Proceedings of Reliability and Maintainability Symposium, Orlando, 2007, pp. 196–201

    Google Scholar 

  5. L.C. Freeman, Centrality in social networks i: conceptual clarification. Soc. Netw. 1(3), 215–239 (1979)

    Article  Google Scholar 

  6. P.K. Srimani, Generalized fault tolerance properties of star graphs source, in Proceedings of the International Conference on Computing and Information, Ottawa, Orlando, 1991, pp. 510–519

    Google Scholar 

  7. M. Duque-Anton, F. Bruyaux, P. Semal, Measuring the survivability of a network: connectivity and rest-connectivity. Europ. Trans. Telecommun. 11(2), 149–158 (2000)

    Article  Google Scholar 

  8. R. Tarjan, Depth first search and linear graph algorithms. SIAM J. Comput. 1, 146–160 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  9. D. Goyal, J. Caffery, Partitioning avoidance in mobile ad hoc networks using network survivability concepts, in Seventh IEEE Symposium on Computers and Communications (ISCC’02), Taormina-Giardini Naxos, Orlando, 2002

    Google Scholar 

  10. M. Hauspie, J. Carle, D. Simplot, Partition detection in mobile ad hoc networksusingmultipledisjointpathsset,in Objects,ModelsandMultimedia Technology Workshop, Switzerland, 2003

    Google Scholar 

  11. M. Jorgic, I. Stojmenovic, M. Hauspie, D. Simplot-Ryl, Localized algorithms for detection of critical nodes and links for connectivity in ad hoc networks, in Proceedings of 3rd IFIP MED-HOC-NET Workshop, Bodrum, 2004

    Google Scholar 

  12. A.L. Barabasi, H. Jeong, Z. Nada, E. Ravasz, A. Schubert, T. Vicsek, Evolution of the social network of scientific collaborations. Phys. A 311, 590 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  13. E. Dahlhaus, D.S. Johnson, C.H. Papadimitriou, P.D. Seymour, M. Yannakakis, The complexity of multiterminal cuts. SIAM J. Comput. 23, 864–894 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  14. L.G. Valiant, Universality considerations in vlsi circuits. IEEE Trans. Comput. 30(2), 135–140 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  15. W. Aiello, F. Chung, L. Lu, A random graph model for massive graphs. in STOC ’00 (ACM, New York, 2000)

    Google Scholar 

  16. A. Ferrante, G. Pandurangan, K. Park, On the hardness of optimization in power-law graphs. Theory. Comput. Sci. 393(1–3), 220–230 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  17. http://en.wikipedia.org/wiki/hopcroft-karp_algorithm

  18. M.R. Garey, D.S. Johnson, The rectilinear steiner tree problem in np complete. SIAM J. Appl. Math. 32, 826–834 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  19. Dénes Kõnig, Gráfok és mátrixok. Matematikai és Fizikai Lapok 38, 116–119 (1931)

    Google Scholar 

  20. J. Håstad, Clique is hard to approximate within n1-, in Proceedings of the 37th Annual Symposium on Foundations of Computer Science (IEEE Computer Society, Washington, DC, 1996), p. 627

    Google Scholar 

  21. M. Stoer, F. Wagner, A simple min-cut algorithm. J. ACM 44(4), 585–591 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  22. D. Wagner, F. Wagner, Between min cut and graph bisection, in MFCS ’93: Proceedings of the 18th International Symposium on Mathematical Foundations of Computer Science (Springer, London, 1993), pp. 744–750

    Google Scholar 

  23. I. Dinur, S. Safra, On the hardness of approximating minimum vertex cover. Ann. Math. 162, 2005 (2004)

    MathSciNet  Google Scholar 

  24. A. Agarwal, M. Charikar, K. Makarychev, Y. Makarychev, O(log n) approximation algorithms for min uncut, min 2cnf deletion, and directed cut problems, in STOC ’05: Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing (ACM, New York 2005), pp. 573–581

    Google Scholar 

  25. G. Even, J.S. Naor, S. Rao, B. Schieber, Divide-and-conquer approximation algorithms via spreading metrics. J. ACM 47(4), 585–616 (2000)

    Article  MathSciNet  Google Scholar 

  26. S. Arora, S. Rao, U. Vazirani, Expander flows, geometric embeddings and graph partitioning, in STOC ’04: Proceedings of the Thirty-Sixth Annual ACM Symposium on Theory of Computing (ACM, New York, 2004), pp. 222–231

    Google Scholar 

  27. S. Arora, E. Hazan, S. Kale, O\((\sqrt{\log n})\) approximation to sparsest cut in \(\tilde{O}({n}^{2})\) time. SIAM J. Comput. 39(5), 1748–1771 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  28. A. Bavelas, A mathematical model for group structure. Human Org. 7, 16–30 (1948)

    Google Scholar 

  29. S.P. Borgatti, M.G. Everett, A graph-theoretic perspective on centrality. Soc. Netw. 28(4), 466–484 (2006)

    Article  Google Scholar 

  30. D. Koschitzki, K.A. Lehmann, S. Peters, L. Richter, D. Tenfelde-Podehl, O. Zlotowski, in Centrality Indices. Lecture Notes in Computer Science, vol. 3418 (Springer, Berlin/New York, 2005) pp. 16–61

    Google Scholar 

  31. A. Karygiannis, E. Antonakakis, A. Apostolopoulos, Detecting critical nodes for manet intrusion detection systems, in Proceedings of Security, Privacy and Trust in Pervasive and Ubiquitous Computing, Lyon, Orlando, 2006

    Google Scholar 

  32. M. Sheng, J. Li, Y. Shi, Critical nodes detection in mobile ad hoc network, in Proceedings of the 20th International Conference on Advanced Information Networking and Applications (AINA’06), Vienna, Orlando, 2006

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Information Science and Engineering, University of Florida, 32611, Gainesville, FL, USA

    M T. Thai, Thang Thang Dinh & Yilin Shen

Authors
  1. M T. Thai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thang Thang Dinh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yilin Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to M T. Thai , Thang Thang Dinh or Yilin Shen .

Editor information

Editors and Affiliations

  1. Department of Industrial and Systems Eng, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  2. Department of Computer Science, University of Texas, Dallas, Richardson, Texas, USA

    Ding-Zhu Du

  3. Dept. Comp. Sci. & Engineering, University of California, San Diego, La Jolla, California, USA

    Ronald L. Graham

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this entry

Cite this entry

Thai, M.T., Dinh, T.T., Shen, Y. (2013). Hardness and Approximation of Network Vulnerability. In: Pardalos, P., Du, DZ., Graham, R. (eds) Handbook of Combinatorial Optimization. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7997-1_23

Download citation

Publish with us

Policies and ethics

Search

Navigation