Rapid Almost-Complete Broadcasting in Faulty Networks

  • Rastislav Královič
  • Richard Královič
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4474)


This paper studies the problem of broadcasting in synchronous point-to-point networks, where one initiator owns a piece of information that has to be transmitted to all other vertices as fast as possible. The model of fractional dynamic faults with threshold is considered: in every step either a fixed number T, or a fraction α, of sent messages can be lost depending on which quantity is larger.

As the main result we show that in complete graphs and hypercubes it is possible to inform all but a constant number of vertices, exhibiting only a logarithmic slowdown, i.e. in time O(Dlogn) where D is the diameter of the network and n is the number of vertices.

Moreover, for complete graphs under some additional conditions (sense of direction, or α< 0.55) the remaining constant number of vertices can be informed in the same time, i.e. O(logn).


Failure Probability Complete Graph Constant Number Edge Connectivity Information Processing Letter 
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.
    Ahlswede, R., et al.: Fault-tolerant minimum broadcast networks. Networks 27 (1996)Google Scholar
  2. 2.
    Bagchi, A., Hakimi, S.L.: Information dissemination in distributed systems with faulty units. IEEE Transactions on Computers 43(6), 698–710 (1994)zbMATHCrossRefGoogle Scholar
  3. 3.
    Berman, K.A., Hawrylycz, M.: Telephone problems with failures. SIAM Journal on Algebraic and Discrete Methods 7(1), 13–17 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Berman, P., Diks, K., Pelc, A.: Reliable broadcasting in logarithmic time with Byzantine link failures. Journal of Algorithms 22(2), 199–211 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Bjork, L.A.: Recovery scenario for a db/dc system. In: ACM’73: Proceedings of the annual conference, pp. 142–146. ACM Press, New York (1973)CrossRefGoogle Scholar
  6. 6.
    Chang, J.-M., Maxemchuk, N.F.: Reliable broadcast protocols. ACM Transactions on Computer Systems 2(3), 251–273 (1984)CrossRefGoogle Scholar
  7. 7.
    Chlebus, B., Diks, K., Pelc, A.: Broadcasting in synchronous networks with dynamic faults. Networks 27 (1996)Google Scholar
  8. 8.
    Chlebus, B.S., Diks, K., Pelc, A.: Optimal broadcasting in faulty hypercubes. In: FTCS, pp. 266–273 (1991)Google Scholar
  9. 9.
    Chung, F.R.K., et al.: On induced subgraphs of the cube. Journal of Combinatorial Theory Series A 49, 180–187 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17(11), 643–644 (1974)zbMATHCrossRefGoogle Scholar
  11. 11.
    Diks, K., Pelc, A.: Almost safe gossiping in bounded degree networks. SIAM Journal on Discrete Mathematics 5(3), 338–344 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Dobrev, S., et al.: On fractional dynamic faults with threshold. In: Flocchini, P., Gąsieniec, L. (eds.) SIROCCO 2006. LNCS, vol. 4056, pp. 197–211. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Dobrev, S., Vrto, I.: Optimal broadcasting in hypercubes with dynamic faults. Information Processing Letters 71(2), 81–85 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Dobrev, S., Vrto, I.: Dynamic faults have small effect on broadcasting in hypercubes. Discrete Applied Mathematics 137(2), 155–158 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Dolev, S.: Self-stabilization. MIT Press, Cambridge (2000)zbMATHGoogle Scholar
  16. 16.
    Fischer, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. Journal of the ACM 32(2), 374–382 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Flocchini, P., Mans, B., Santoro, N.: On the impact of sense of direction on message complexity. Information Processing Letters 63(1), 23–31 (1997)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Santoro, N., Mans, B., Flocchini, P.: Sense of Direction in Distributed Computing. In: Kutten, S. (ed.) DISC 1998. LNCS, vol. 1499, pp. 1–15. Springer, Heidelberg (1998)Google Scholar
  19. 19.
    Fraigniaud, P.: Asymptotically optimal broadcasting and gossiping in faulty hypercube multicomputers. IEEE Transactions on Computers 41(11), 1410–1419 (1992)CrossRefGoogle Scholar
  20. 20.
    Gasieniec, L., Pelc, A.: Broadcasting with linearly bounded transmission faults. Discrete Applied Mathematics 83(1-3), 121–133 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Hedetniemi, S., Hedetniemi, S., Liestman, A.: A survey of broadcasting and gossiping in communication networks. Networks 18, 319–349 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Královič, R.,  Královič, R.,  Ružička, P.: Broadcasting with many faulty links. In: Sibeyn, J.F. (ed) SIROCCO, of Proceedings in Informatics, vol. 17, pp. 211–222. Carleton Scientific (2003)Google Scholar
  23. 23.
    Královič, R., Královič, R.: Rapid almost-complete broadcasting in faulty networks. Technical report, arXiv:cs.DC/0703122 (2007)Google Scholar
  24. 24.
    Liptak, Z., Nickelsen, A.: Broadcasting in complete networks with dynamic edge faults. In: Butelle, F. (ed.) OPODIS, Studia Informatica Universalis, pp. 123–142. Suger, Saint-Denis, rue Catulienne, France (2000)Google Scholar
  25. 25.
    Pease, M., Shostak, R., Lamport, L.: Reaching agreement in the presence of faults. Journal of the ACM 27(2), 228–234 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Pelc, A.: Broadcasting in complete networks with faulty nodes using unreliable calls. Information Processing Letters 40(3), 169–174 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Pelc, A., Peleg, D.: Feasibility and complexity of broadcasting with random transmission failures. In: PODC ’05: Proceedings of the twenty-fourth annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing, pp. 334–341. ACM Press, New York (2005)CrossRefGoogle Scholar
  28. 28.
    Santoro, N., Widmayer, P.: Distributed function evaluation in the presence of transmission faults. In: Asano, T., et al. (eds.) SIGAL 1990. LNCS, vol. 450, pp. 358–367. Springer, Heidelberg (1990)Google Scholar
  29. 29.
    Stanoi, I., Agrawal, D., Abbadi, A.E.: Using broadcast primitives in replicated databases. In: ICDCS ’98: Proceedings of the The 18th International Conference on Distributed Computing Systems, pp. 148–155. IEEE Computer Society, Washington (1998)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Rastislav Královič
    • 1
  • Richard Královič
    • 1
    • 2
  1. 1.Department of Computer Science, Comenius University, Mlynská dolina, 84248 BratislavaSlovakia
  2. 2.Department of Computer Science, ETH ZurichSwitzerland

Personalised recommendations