Distributed Computing

, Volume 28, Issue 6, pp 407–422 | Cite as

Randomized broadcast in radio networks with collision detection

  • Mohsen Ghaffari
  • Bernhard Haeupler
  • Majid Khabbazian
Article

Abstract

We present a randomized distributed algorithm that in radio networks with collision detection broadcasts a single message in \(O(D + \log ^6 n)\) rounds, with high probability. This time complexity is most interesting because of its optimal additive dependence on the network diameter \(D\). It improves over the currently best known \(O(D\log \frac{n}{D}\,+\,\log ^2 n)\) algorithms, due to Czumaj and Rytter (Broadcasting algorithms in radio networks with unknown topology. In: Proceedings of the symposium on foundations of computer science, pp 492–501, 2003), and Kowalski and Pelc (Broadcasting in undirected ad hoc radio networks. In: Proceedings of the ACM SIGACT-SIGOPS symposium on principles of distributed computing, pp 73–82, 2003). These algorithms where designed for the model without collision detection and are optimal in that model. However, as explicitly stated by Peleg in his 2007 survey on broadcast in radio networks, it had remained an open question whether the bound can be improved with collision detection. We also study distributed algorithms for broadcasting \(k\) messages from a single source to all nodes. This problem is a natural and important generalization of the single-message broadcast problem, but is in fact considerably more challenging and less understood. We show the following results: If the network topology is known to all nodes, then a \(k\)-message broadcast can be performed in \(O(D + k\log n + \log ^2 n)\) rounds, with high probability. If the topology is not known, but collision detection is available, then a \(k\)-message broadcast can be performed in \(O(D + k\log n + \log ^6 n)\) rounds, with high probability. The first bound is optimal and the second is optimal modulo the additive \(O(\log ^6 n)\) term.

Keywords

Wireless networks Radio networks Broadcast Collision detection Random linear network coding 

References

  1. 1.
    Alon, N., Bar-Noy, A., Linial, N., Peleg, D.: A lower bound for radio broadcast. J. Comput. Syst. Sci. 43(2), 290–298 (1991)MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Alon, N., Ghaffari, M., Haeupler, B., Khabbazian, M.: Broadcast throughput in radio networks: routing vs. network coding. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, pp. 1831–1843 (2014)Google Scholar
  3. 3.
    Bar-Yehuda, R., Goldreich, O., Itai, A.: On the time-complexity of broadcast in multi-hop radio networks: an exponential gap between determinism and randomization. J. Comput. Syst. Sci. 45(1), 104–126 (1992)Google Scholar
  4. 4.
    Bar-Yehuda, R., Israeli, A., Itai, A.: Multiple communication in multi-hop radio networks. SIAM J. Comput. 22(4), 875–887 (1993)MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Chlamtac, I., Kutten, S.: On broadcasting in radio networks: problem analysis and protocol design. IEEE Trans. Commun. 33(12), 1240–1246 (1985)MATHCrossRefGoogle Scholar
  6. 6.
    Chlebus, B., Kowalski, D., Pelc, A., Rokicki, M.A.: Efficient distributed communication in ad-hoc radio networks. In: Proceedings of the International Conference on Automata, Languages and Programming, pp. 613–624 (2011)Google Scholar
  7. 7.
    Czumaj, A., Rytter, W.: Broadcasting algorithms in radio networks with unknown topology. In: Proceedings of the Symposium on Foundations of Computer Science, pp. 492–501 (2003)Google Scholar
  8. 8.
    Gasieniec, L., Peleg, D., Xin, Q.: Faster communication in known topology radio networks. In: Proceedings of the ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, pp. 129–137 (2005)Google Scholar
  9. 9.
    Gasieniec, L., Potapov, I.: Gossiping with unit messages in known radio networks. In: IFIP TCS, pp. 193–205 (2002)Google Scholar
  10. 10.
    Ghaffari, M., Haeupler, B.: Fast structuring of radio networks for multi-message communications. In: Proceedings of the International Symposium on Distributed Computing (2013)Google Scholar
  11. 11.
    Ghaffari, M., Haeupler, B.: Near optimal leader election in multi-hop radio networks. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, pp. 748–766 (2013)Google Scholar
  12. 12.
    Haeupler, B.: Analyzing network coding gossip made easy. In: Proceedings of the Symposium on Theory of Computing, STOC’11, pp. 293–302 (2011)Google Scholar
  13. 13.
    Haeupler, B., Kim, M., Medard, M.: Optimality of network coding with buffers. In: Proceedings of the IEEE Information Theory Workshop, pp. 533–537 (2011)Google Scholar
  14. 14.
    Ho, T., Koetter, R., Medard, M., Karger, D., Effros, M.: The benefits of coding over routing in a randomized setting. In: Proceedings of the IEEE International Symposium on Information Theory (2003)Google Scholar
  15. 15.
    Khabbazian, M., Kowalski, D.: Time-efficient randomized multiple-message broadcast in radio networks. In: Proceedings of the ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, pp. 373–380 (2011)Google Scholar
  16. 16.
    Kowalski, D., Pelc, A.: Broadcasting in undirected ad hoc radio networks. In: Proceedings of the ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, pp. 73–82 (2003)Google Scholar
  17. 17.
    Kowalski, D., Pelc, A.: Optimal deterministic broadcasting in known topology radio networks. Distrib. Comput. 19(3), 185–195 (2007)CrossRefGoogle Scholar
  18. 18.
    Kushilevitz, E., Mansour, Y.: An \({\Omega }(D\log (N/D))\) lower bound for broadcast in radio networks. In: Proceedings of the ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, pp. 65–74 (1993)Google Scholar
  19. 19.
    Manne, F., Xin, Q.: Optimal gossiping with unit size messages in known topology radio networks. In: Proceedings of the Workshop on Combinatorial and Algorithmic Aspects of Networking, pp. 125–134 (2006)Google Scholar
  20. 20.
    Peleg, D.: Time-efficient broadcasting in radio networks: a review. In: Proceedings of the International Conference on Distributed Computing and Internet Technologies, pp. 1–18 (2007)Google Scholar
  21. 21.
    Schneider, J., Wattenhofer, R.: What is the use of collision detection (in wireless networks)?. In: Proceedings of the 24th International Conference on Distributed Computing, pp. 133–147 (2010)Google Scholar
  22. 22.
    Xin, Q.: Personal communication (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Mohsen Ghaffari
    • 1
  • Bernhard Haeupler
    • 2
  • Majid Khabbazian
    • 3
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA
  2. 2.Carnegie Mellon UniversityPittsburghUSA
  3. 3.University of AlbertaEdmontonCanada

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