Discovering Network Topology in the Presence of Byzantine Faults

  • Mikhail Nesterenko
  • Sébastien Tixeuil
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4056)


We study the problem of Byzantine-robust topology discovery in an arbitrary asynchronous network. We formally state the weak and strong versions of the problem. The weak version requires that either each node discovers the topology of the network or at least one node detects the presence of a faulty node. The strong version requires that each node discovers the topology regardless of faults.

We focus on non-cryptographic solutions to these problems. We explore their bounds. We prove that the weak topology discovery problem is solvable only if the connectivity of the network exceeds the number of faults in the system. Similarly, we show that the strong version of the problem is solvable only if the network connectivity is more than twice the number of faults.

We present solutions to both versions of the problem. Our solutions match the established graph connectivity bounds. The programs are terminating, they do not require the individual nodes to know either the diameter or the size of the network. The message complexity of both programs is low polynomial with respect to the network size.


Message Complexity Faulty Node System Topology Faulty Process Path Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Spinelli, J.M., Gallager, R.G.: Event-driven topology broadcast without sequence numbers. IEEE trans. on commun. COM-37(5), 468–474 (1989)CrossRefGoogle Scholar
  2. 2.
    Hill, J., Culler, D.: Mica: A wireless platform for deeply embedded networks. IEEE Micro 22, 12–24 (2002)CrossRefGoogle Scholar
  3. 3.
    Lamport, L., Shostak, R., Pease, M.: The byzantine generals problem. ACM Transactions on Programming Languages and Systems 4, 382–401 (1982)zbMATHCrossRefGoogle Scholar
  4. 4.
    Avramopoulos, I.C., Kobayashi, H., Wang, R., Krishnamurthy, A.: Highly secure and efficient routing. In: Proceedings of INFOCOM: The Conference on Computer Communications, joint conference of the IEEE Computer and Communications Societies, Hong Kong (2004)Google Scholar
  5. 5.
    Perrig, A., Stankovic, J., Wagner, D.: Security in wireless sensor networks. Communications of the ACM 47, 53–57 (2004)CrossRefGoogle Scholar
  6. 6.
    Bhandari, V., Vaidya, N.H.: On reliable broadcast in a radio network. In: Proceedings of the Twenty-Fourth Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing (PODC 2005), Las Vegas, Nevada (to appear, 2005)Google Scholar
  7. 7.
    Dolev, D.: The Byzantine generals strike again. Journal of Algorithms 3, 14–30 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Koo, C.Y.: Broadcast in radio networks tolerating byzantine adversarial behavior. In: PODC 2004: Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing, pp. 275–282. ACM Press, New York (2004)CrossRefGoogle Scholar
  9. 9.
    Pelc, A., Peleg, D.: Broadcasting with locally bounded byzantine faults. Information Processing Letters 93, 109–115 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Attiya, H., Welch, J.: Distributed Computing: Fundamentals, Simulations, and Advanced Topics, p. 6. McGraw-Hill Publishing Company, New York (1998)Google Scholar
  11. 11.
    Malkhi, D., Reiter, M., Rodeh, O., Sella, Y.: Efficient update diffusion in byzantine environments. In: The 20th IEEE Symposium on Reliable Distributed Systems (SRDS 2001), pp. 90–98. IEEE, Washington - Brussels - Tokyo (2001)Google Scholar
  12. 12.
    Malkhi, D., Mansour, Y., Reiter, M.K.: Diffusion without false rumors: on propagating updates in a Byzantine environment. Theoretical Computer Science 299, 289–306 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Minsky, Y., Schneider, F.B.: Tolerating malicious gossip. Distributed Computing 16, 49–68 (2003)CrossRefGoogle Scholar
  14. 14.
    Masuzawa, T., Tixeuil, S.: A self-stabilizing link-coloring protocol resilient to unbounded byzantine faults in arbitrary networks. Technical Report 1396, Laboratoire de Recherche en Informatique (2005)Google Scholar
  15. 15.
    Nesterenko, M., Arora, A.: Tolerance to unbounded byzantine faults. In: Proceedings of 21st IEEE Symposium on Reliable Distributed Systems, pp. 22–29 (2002)Google Scholar
  16. 16.
    Sakurai, Y., Ooshita, F., Masuzawa, T.: A self-stabilizing link-coloring protocol resilient to byzantine faults in tree networks. In: Higashino, T. (ed.) OPODIS 2004. LNCS, vol. 3544, pp. 283–298. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    Masuzawa, T.: A fault-tolerant and self-stabilizing protocol for the topology problem. In: Proceedings of the Second Workshop on Self-Stabilizing Systems, vol. 1, pp. 1.1–1.15 (1995)Google Scholar
  18. 18.
    Yellen, J., Gross, J.L.: Graph Theory & Its Applications. CRC Press, Boca Raton (1998), ISBN: 0–849–33982–0Google Scholar
  19. 19.
    Dijkstra, E.W., Scholten, C.S.: Predicate Calculus and Program Semantics. Springer, Berlin (1990)zbMATHGoogle Scholar
  20. 20.
    Nesterenko, M., Tixeuil, S.: Bounds on topology discovery in the presence of byzantine faults. Technical Report TR-KSU-CS-2006-01, Dept. of Computer Science, Kent State University (2006),
  21. 21.
    Nesterenko, M., Tixeuil, S.: Discovering network topology in the presence of byzantine faults. Technical Report TR-KSU-CS-2005-01, Dept. of Computer Science, Kent State University (2005),
  22. 22.
    Dijkstra, E., Scholten, C.: Termination detection for diffusing computations. Information Processing Letters 11, 1–4 (1980)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Mikhail Nesterenko
    • 1
  • Sébastien Tixeuil
    • 2
  1. 1.Computer Science DepartmentKent State UniversityKentUSA
  2. 2.LRI-CNRS UMR 8623 & INRIA Grand LargeUniversité Paris SudFrance

Personalised recommendations