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Cardinality-Constrained Critical Node Detection Problem

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Performance Models and Risk Management in Communications Systems

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 46))

Abstract

We consider methodologies for managing risk in a telecommunication network based on identification of the critical nodes. The objective is to minimize the number of vertices whose deletion results in disconnected components which are constrained by a given cardinality. This is referred to as the CARDINALITY CONSTRAINED CRITICAL NODE PROBLEM (CC-CNP), and finds application in epidemic control, telecommunications, and military tactical planning, among others. From a telecommunication perspective, the set of critical nodes helps determine which players should be removed from the network in the event of a virus outbreak. Conversely, in order to maintain maximum global connectivity, it should be ensured that the critical nodes remain intact and as secure as possible. The presence of these nodes make a network vulnerable to attacks as they are crucial for the overall connectivity. This is a variation of the CRITICAL NODE DETECTION PROBLEM which has a known complexity and heuristic procedure. In this chapter, we review the recent work in this area, provide formulations based on integer linear programming and develop heuristic procedures for CC-CNP. We also examine the relations of CC-CNP with the well known NODE DELETION PROBLEM and discuss complexity results as a result of this relation.

Date: Feb 2009.

This project was partially funded by Air Force Research Laboratory.

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References

  1. Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows: Theory, algorithms, and applications. Prentice-Hall, Englewood Cliffs, NJ

    MATH  Google Scholar 

  2. Arulselvan A, Commander CW, Elefteriadou L, Pardalos PM (2009) Detecting critical nodes in sparse graphs. Comput Oper Res, 36(7):2193–2200

    Article  MATH  MathSciNet  Google Scholar 

  3. Bavelas A (1948) A mathematical model for group structure. Hum Org 7:16–30

    Google Scholar 

  4. Borgatti SP (2006) Identifying sets of key players in a network. Comput Math Org Theory 12(1):21–34

    Article  MATH  Google Scholar 

  5. Cohen R, Erez K, ben Avraham D, Havlin S (2000) Efficient immunization strategies for computer networks and populations. Phys Rev Lett 85:4626

    Article  Google Scholar 

  6. Coley DA (1999) An introduction to genetic algorithms for scientists and engineers. World Scientific, Singapore

    Google Scholar 

  7. Freeman LC (1979) Centrality in social networks I: Conceptual clarification. Social Netw 1:215–239

    Article  Google Scholar 

  8. Garey MR, Johnson DS (1979) Computers and intractability: A guide to the theory of NP-completeness. W.H. Freeman, New York

    MATH  Google Scholar 

  9. Glover F, Laguna M, Martí R (2000) Fundamentals of scatter search and path-relinking. Contr Cybernet 39:653–684

    Google Scholar 

  10. Harper PR, de Senna V, Vieira IT, Shahani AK (2005) A genetic algorithm for the project assignment problem. Comput Oper Res 32:1255–1265

    Article  MATH  Google Scholar 

  11. Krebs V (2002) Uncloaking terrorist networks. First Monday 7(4) http://www.firstmonday.dk/issue74/krebs/index.html

  12. Krishnamoorthy MS, Deo N (1979) Node-deletion NP-complete problems. SIAM J Comput 8(4):619–625

    Article  MATH  MathSciNet  Google Scholar 

  13. Lewis J, Yannakakis M (1980) The node-deletion problem for hereditary properties is NP-complete. J Comput Syst Sci 20(2):219–230

    Article  MATH  MathSciNet  Google Scholar 

  14. Lund C, Yannakakis M (1993) The approximation of maximum subgraph problems. In: ICALP ’93: Proceedings of the 20th International Colloquium on Automata, Languages and Programming, London, UK. Springer, Berlin, pp 40–51

    Google Scholar 

  15. Mitchell M (1996) An introduction to genetic algorithms. MIT, Cambridge, MA

    Google Scholar 

  16. Oliveira CAS, Pardalos PM, Querido TM (2004) Integer formulations for the message scheduling problem on controller area networks. In: Grundel D, Murphey R, Pardalos P (eds) Theory and algorithms for cooperative systems. World Scientific, Singapore, pp 353–365

    Chapter  Google Scholar 

  17. Resende MGC, Werneck RF (2006) A hybrid multistart heuristic for the uncapacitated facility location problem. Eur J Oper Res 174:54–68

    Article  MATH  MathSciNet  Google Scholar 

  18. Resende MGC, Werneck RF (2007) A fast swap-based local search procedure for location problems. Ann Oper Res. doi: 10.1007/s10479–006–0154–0

    Google Scholar 

  19. Spears WM, DeJong KA (1991) On the virtues of parameterized uniform crossover. In Proceedings of the 4th International Conference on Genetic Algorithms, San Diego, CA, USA, pp 230–236

    Google Scholar 

  20. Wislon JM (1997) A genetic algorithm for the generalised assignment problem. J Oper Res Soc 48:804–809

    Article  Google Scholar 

  21. Zhou T, Fu Z-Q, Wang B-H (2006) Epidemic dynamics on complex networks. Progr Nat Sci 16(5):452–457

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Center for Discrete Mathematics and Applications, Warwick Business School, University of Warwick, Coventry, UK

    Ashwin Arulselvan

  2. Air Force Research Laboratory, Munitions Directorate, and Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Clayton W. Commander

  3. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Oleg Shylo & Panos M. Pardalos

Authors
  1. Ashwin Arulselvan
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  2. Clayton W. Commander
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  3. Oleg Shylo
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  4. Panos M. Pardalos
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Corresponding authors

Correspondence to Ashwin Arulselvan , Clayton W. Commander , Oleg Shylo or Panos M. Pardalos .

Editor information

Editors and Affiliations

  1. The University of Warwick, Warwick Business School, Coventry, CV4 7AL, United Kingdom

    Nalân Gülpınar

  2. , Department of Computing, Imperial College London, Queen's Gate 180, London, SW7 2BZ, United Kingdom

    Peter Harrison

  3. , Department of Computing, Imperial College London, Queen's Gate 180, London, SW7 2BZ, United Kingdom

    Berç Rüstem

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Arulselvan, A., Commander, C.W., Shylo, O., Pardalos, P.M. (2011). Cardinality-Constrained Critical Node Detection Problem. In: Gülpınar, N., Harrison, P., Rüstem, B. (eds) Performance Models and Risk Management in Communications Systems. Springer Optimization and Its Applications, vol 46. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0534-5_4

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