Skip to main content
SpringerLink
Log in

Design of Network Topology in an Adversarial Environment

  • Conference paper
Decision and Game Theory for Security (GameSec 2010)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6442))

Included in the following conference series:

Abstract

We study the strategic interaction between a network manager whose goal is to choose (as communication infrastructure) a spanning tree of a network given as an undirected graph, and an attacker who is capable of attacking a link in the network. We model their interaction as a zero-sum game and discuss a particular set of Nash equilibria. More specifically, we show that there always exists a Nash equilibrium under which the attacker targets a critical set of links. A set of links is called critical if it has maximum vulnerability, and the vulnerability of a set of links is defined as the minimum fraction of links the set has in common with a spanning tree. Using simple examples, we discuss the importance of critical subsets in the design of networks that are aimed to be robust against attackers. Finally, an algorithm is provided, to compute a critical subset of a given graph.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Awerbuch, B., Richa, A., Scheideler, C.: A Jamming-Resistant MAC Protocol for Single-Hop Wireless Networks. In: PODC 2008: Proceedings of the 27th ACM Symposium on Principles of Distributed Computing, pp. 45–54 (2008)

    Google Scholar 

  2. Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (March 2004)

    Book  MATH  Google Scholar 

  3. Catlin, P.A., Lai, H.-J., Shao, Y.: Edge-Connectivity and Edge-Disjoint Spanning Trees. Discrete Mathematics 309(5), 1033–1040 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chopra, S.: On the Spanning Tree Polyhedron. Operations Research Letters 8(1), 25–29 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  5. Commander, C.W., Pardalos, P.M., Ryabchenko, V., Uryasev, S., Zrazhevsky, G.: The Wireless Network Jamming Problem. J. Comb. Optim. 14(4), 481–498 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cordovil, R., Fukuda, K., Moreira, M.L.: Clutters and Matroids. Discrete Math. 89(2), 161–171 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cornuejols, G.: Combinatorial Optimization: Packing and Covering. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (2001)

    Book  MATH  Google Scholar 

  8. Cunningham, W.H.: Optimal Attack and Reinforcement of a Network. J. ACM 32(3), 549–561 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  9. Edmonds, J., Fulkerson, D.R.: Bottleneck Extrema. Journal of Combinatorial Theory (8), 299–306 (1970)

    Google Scholar 

  10. Fulkerson, D.R.: Blocking and Anti-Blocking Pairs of Polyhedra. Math. Programming (1), 168–194 (1971)

    Google Scholar 

  11. Gueye, A., Walrand, J.C., Anantharam, V.: Understanding the Design of Network Topology in Adversarial Environment (2010), http://www.eecs.berkeley.edu/~agueye/index.html

  12. Gupta, A., Kumar, A., Pal, M., Roughgarden, T.: Approximation Via Cost-Sharing: A Simple Approximation Algorithm for the Multicommodity Rent-or-Buy Problem. J. ACM 54(3), 11 (2007)

    Article  Google Scholar 

  13. Gusfield, D.: Connectivity and Edge-Disjoint Spanning Trees. Information Processing Letters (16), 87–89 (1983)

    Google Scholar 

  14. Karger, D.R., Stein, C.: An o(n2) Algorithm for Minimum Cuts, New York, NY, USA, pp. 757–765 (1993)

    Google Scholar 

  15. Kruskal, J., Joseph, B.: On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem. Proceedings of the American Mathematical Society 7(1), 48–50 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  16. Fulkerson, D., Ford, L.: Flows in Networks, pp. 453–460. Princeton Univ. Press, Princeton (1962)

    MATH  Google Scholar 

  17. Matveev, A.O.: Maps on Posets, and Blockers. ArXiv Mathematics e-prints (November 2004)

    Google Scholar 

  18. Matveev, A.O.: On Blockers in Bounded Posets. Int. J. Math. Math. Sci. (26), 581–588

    Google Scholar 

  19. Nash-Williams, J.A.: Edge-Disjoint Spanning Trees of Finite Graphs. Journal London Math. Soc. (36), 445–450 (1961)

    Google Scholar 

  20. Prim, R.C.: Shortest Connection Networks and some Generalizations. Bell System Technology Journal 36, 1389–1401 (1957)

    Article  Google Scholar 

  21. Robert, V.: Linear Programming: Foundations and Extensions. Springer, Heidelberg (2001)

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  23. Tutte, W.T.: On the Problem of Decomposing a Graph into N Connected Factors. Journal of the London Mathematical Society (36), 221–230 (1961)

    Google Scholar 

  24. Neumann, J.v.: Zur Theorie der Gesellschaftspiele. Mathematische Annalen 100, 295–320 (1928)

    Article  MathSciNet  Google Scholar 

  25. Welsh, D.: Matroid Theory. Academic Press, New York (1976)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. EECS Department, University of California at Berkeley, Berkeley, CA, 94720, USA

    Assane Gueye, Jean C. Walrand & Venkat Anantharam

Authors
  1. Assane Gueye
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jean C. Walrand
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Venkat Anantharam
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Deutsche Telekom Laboratories, Technische Universität Berlin, 10587, Berlin, Germany

    Tansu Alpcan

  2. Laboratory of Cryptography and System Security (CrySyS), Budapest University of Technology and Economics, Budapest, Hungary

    Levente Buttyán

  3. Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, USA

    John S. Baras

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gueye, A., Walrand, J.C., Anantharam, V. (2010). Design of Network Topology in an Adversarial Environment. In: Alpcan, T., Buttyán, L., Baras, J.S. (eds) Decision and Game Theory for Security. GameSec 2010. Lecture Notes in Computer Science, vol 6442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17197-0_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-17197-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17196-3

  • Online ISBN: 978-3-642-17197-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation