Agreement in Directed Dynamic Networks

  • Martin Biely
  • Peter Robinson
  • Ulrich Schmid
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7355)


We study the fundamental problem of achieving consensus in a synchronous dynamic network, where an omniscient adversary controls the unidirectional communication links. Its behavior is modeled as a sequence of directed graphs representing the active (i.e. timely) communication links per round. We prove that consensus is impossible under some natural weak connectivity assumptions, and introduce vertex-stable root components as a—practical and not overly strong—means for circumventing this impossibility. Essentially, we assume that there is a short period of time during which an arbitrary part of the network remains strongly connected, while its interconnect topology keeps changing continuously. We present a consensus algorithm that works under this assumption, and prove its correctness. Our algorithm maintains a local estimate of the communication graphs, and applies techniques for detecting stable network properties and univalent system configurations. Our possibility results are complemented by several impossibility results and lower bounds, which reveal that our algorithm is asymptotically optimal.


Dynamic Network Impossibility Result Communication Graph Consensus Algorithm Transmission Failure 
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.
    Goiser, A., Khattab, S., Fassl, G., Schmid, U.: A new robust interference reduction scheme for low complexity direct-sequence spread-spectrum receivers: Performance. In: Proceedings 3rd International IEEE Conference on Communication Theory, Reliability, and Quality of Service (CTRQ 2010), pp. 15–21 (June 2010)Google Scholar
  2. 2.
    Ware, C., Judge, J., Chicharo, J., Dutkiewicz, E.: Unfairness and capture behaviour in 802.11 adhoc networks. In: 2000 IEEE International Conference on Communications, ICC 2000. Global Convergence Through Communications (2000)Google Scholar
  3. 3.
    Kuhn, F., Oshman, R., Moses, Y.: Coordinated consensus in dynamic networks. In: Proceedings of the 30th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2011. ACM (2011)Google Scholar
  4. 4.
    Biely, M., Robinson, P., Schmid, U.: Agreement in directed dynamic networks. CoRR abs/1204.0641 (2012)Google Scholar
  5. 5.
    Biely, M., Robinson, P., Schmid, U.: Solving k-set agreement with stable skeleton graphs. In: IPDPS Workshops, pp. 1488–1495 (2011)Google Scholar
  6. 6.
    Afek, Y., Gafni, E., Rosen, A.: The slide mechanism with applications in dynamic networks. In: ACM PODC, pp. 35–46 (1992)Google Scholar
  7. 7.
    Awerbuch, B., Patt-Shamir, B., Peleg, D., Saks, M.E.: Adapting to asynchronous dynamic networks. In: STOC 1992, pp. 557–570 (1992)Google Scholar
  8. 8.
    Harary, F., Gupta, G.: Dynamic graph models. Mathematical and Computer Modelling 25, 79–87 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Kuhn, F., Oshman, R.: Dynamic networks: Models and algorithms. SIGACT News 42(1), 82–96 (2011)CrossRefGoogle Scholar
  10. 10.
    Casteigts, A., Flocchini, P., Quattrociocchi, W., Santoro, N.: Time-Varying Graphs and Dynamic Networks. In: Frey, H., Li, X., Ruehrup, S. (eds.) ADHOC-NOW 2011. LNCS, vol. 6811, pp. 346–359. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Kuhn, F., Lynch, N., Oshman, R.: Distributed computation in dynamic networks. In: ACM STOC, pp. 513–522 (2010)Google Scholar
  12. 12.
    Santoro, N., Widmayer, P.: Time is Not a Healer. In: Cori, R., Monien, B. (eds.) STACS 1989. LNCS, vol. 349, pp. 304–313. Springer, Heidelberg (1989)CrossRefGoogle Scholar
  13. 13.
    Charron-Bost, B., Schiper, A.: The Heard-Of model: computing in distributed systems with benign faults. Distributed Computing 22(1), 49–71 (2009)CrossRefGoogle Scholar
  14. 14.
    Biely, M., Charron-Bost, B., Gaillard, A., Hutle, M., Schiper, A., Widder, J.: Tolerating corrupted communication. In: Proceedings of the 26th ACM Symposium on Principles of Distributed Computing (PODC 2007), pp. 244–253. ACM (2007)Google Scholar
  15. 15.
    Gafni, E.: Round-by-round fault detectors (extended abstract): unifying synchrony and asynchrony. In: Proceedings of the Seventeenth Annual ACM Symposium on Principles of Distributed Computing, pp. 143–152. ACM Press (1998)Google Scholar
  16. 16.
    Schmid, U., Weiss, B., Keidar, I.: Impossibility results and lower bounds for consensus under link failures. SIAM Journal on Computing 38(5), 1912–1951 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Biely, M., Schmid, U., Weiss, B.: Synchronous consensus under hybrid process and link failures. Theoretical Computer Science 412(40), 5602–5630 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Peleg, D.: Distributed Computing: A Locality-Sensitive Approach. SIAM Monographs on Discrete Mathematics ans Applications, Philadelphia (2000)Google Scholar
  19. 19.
    Elrad, T., Francez, N.: Decomposition of distributed programs into communication-closed layers. Science of Computer Programming 2(3), 155–173 (1982)zbMATHCrossRefGoogle Scholar
  20. 20.
    Lamport, L.: Time, clocks, and the ordering of events in a distributed system. Commun. ACM 21(7), 558–565 (1978)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Martin Biely
    • 1
  • Peter Robinson
    • 2
  • Ulrich Schmid
    • 3
  1. 1.EPFLSwitzerland
  2. 2.Division of Mathematical SciencesNanyang Technological UniversitySingapore
  3. 3.Embedded Computing Systems Group (E182/2)Technische Universität WienViennaAustria

Personalised recommendations