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Efficient Symmetry Breaking in Multi-Channel Radio Networks

  • Sebastian Daum
  • Fabian Kuhn
  • Calvin Newport
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7611)

Abstract

We investigate the complexity of basic symmetry breaking problems in multihop radio networks with multiple communication channels. We assume a network of synchronous nodes, where each node can be awakened individually in an arbitrary time slot by an adversary. In each time slot, each awake node can transmit or listen (without collision detection) on one of multiple available shared channels. The network topology is assumed to satisfy a natural generalization of the well-known unit disk graph model.

We study the classic wake-up problem and a new variant we call active wake-up. For the former we prove a lower bound that shows the advantage of multiple channels disappears for any network of more than one hop. For the active version however, we describe an algorithm that outperforms any single channel solution. We then extend this algorithm to compute a constant approximation for the minimum dominating set (MDS) problem in the same time bound. Combined, these results for the increasingly relevant multi-channel model show that it is often possible to leverage channel diversity to beat classic lower bounds, but not always.

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References

  1. 1.
    I. 802.11. Wireless LAN MAC and Physical Layer Specifications (June 1999)Google Scholar
  2. 2.
    Alon, N., Bar-Noy, A., Linial, N., Peleg, D.: A Lower Bound for Radio Broadcast. Journal of Computer and System Sciences 43(2), 290–298 (1991)MathSciNetzbMATHCrossRefGoogle 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. Journal of Computer and System Sciences 45(1), 104–126 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Barriére, L., Fraigniaud, P., Narayanan, L.: Robust position-based routing in wireless ad hoc networks with unstable transmission ranges. In: Proc. 5th Int. Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications (DIALM), pp. 19–27 (2001)Google Scholar
  5. 5.
    Bluetooth Consortium. Bluetooth Specification Version 2.1 (July 2007)Google Scholar
  6. 6.
    Bonis, A.D., Gasieniec, L., Vaccaro, U.: Generalized fFamework for Selectors with Applications in Optimal Group Testing. In: Proceedings of the International Colloquium on Automata, Languages and Programming (2003)Google Scholar
  7. 7.
    Chlamtac, I., Kutten, S.: On Broadcasting in Radio Networks–Problem Analysis and Protocol Design. IEEE Transactions on Communications 33(12), 1240–1246 (1985)zbMATHCrossRefGoogle Scholar
  8. 8.
    Chlebus, B.S., Kowalski, D.R.: A Better Wake-Up in Radio Networks. In: Proceedings of the ACM Symposium on Principles of Distributed Computing, pp. 266–274. ACM (2004)Google Scholar
  9. 9.
    Chrobak, M., Gasieniec, L., Kowalski, D.: The Wake-Up Problem in Multi-Hop Radio Networks. In: Proceedings of the Annual Symposium on Discrete Algorithms, pp. 992–1000. Society for Industrial and Applied Mathematics (2004)Google Scholar
  10. 10.
    Clementi, A.E.F., Monti, A., Silvestri, R.: Distributed Broadcast in Radio Networks of Unknown Topology. Theoretical Computer Science 302(1-3) (2003)Google Scholar
  11. 11.
    Daum, S., Gilbert, S., Kuhn, F., Newport, C.: Leader Election in Shared Spectrum Networks. In: Proceedings of the Principles of Distributed Computing (to appear, 2012)Google Scholar
  12. 12.
    Daum, S., Kuhn, F., Newport, C.: Efficient Symmetry Breaking in Multi-Channel Radio Networks. Technical Report 271, University of Freiburg, Dept. of Computer Science (2012)Google Scholar
  13. 13.
    Farach-Colton, M., Fernandes, R.J., Mosteiro, M.A.: Lower Bounds for Clear Transmissions in Radio Networks. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 447–454. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Gasieniec, L., Pelc, A., Peleg, D.: The Wakeup Problem in Synchronous Broadcast Systems. In: Proceedings of the ACM Symposium on Principles of Distributed Computing, pp. 113–121 (2000)Google Scholar
  15. 15.
    Jurdzinski, T., Stachowiak, G.: Probabilistic Algorithms for the Wakeup Problem in Single-Hop Radio Networks. In: Proceedings of the International Symposium on Algorithms and Computation, pp. 535–549 (2002)Google Scholar
  16. 16.
    Kuhn, F., Moscibroda, T., Wattenhofer, R.: Initializing Newly Deployed Ad Hoc and Sensor Networks. In: Proceedings of International Conference on Mobile Computing and Networking, pp. 260–274. ACM (2004)Google Scholar
  17. 17.
    Kuhn, F., Moscibroda, T., Wattenhofer, R.: On the locality of bounded growth. In: Proc. 24th Symp. on Principles of Distributed Computing (PODC), pp. 60–68 (2005)Google Scholar
  18. 18.
    Kuhn, F., Wattenhofer, R., Zollinger, A.: Ad hoc networks beyond unit disk graphs. Wireless Networks 14(5), 715–729 (2008)CrossRefGoogle Scholar
  19. 19.
    Kushilevitz, E., Mansour, Y.: An (D log (N/D)) Lower Bound for Broadcast in Radio Networks. SIAM Journal on Computing 27(3), 702–712 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Moscibroda, T., Wattenhofer, R.: Maximal independent sets in radio networks. In: Proc. 24th Symp. on Principles of Distributed Computing (PODC), pp. 148–157 (2005)Google Scholar
  21. 21.
    Schmid, S., Wattenhofer, R.: Algorithmic models for sensor networks. In: Proc. 14th Int. Workshop on Parallel and Distributed Real-Time Systmes, pp. 1–11 (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sebastian Daum
    • 1
  • Fabian Kuhn
    • 2
  • Calvin Newport
    • 3
  1. 1.Faculty of InformaticsUniversity of LuganoSwitzerland
  2. 2.Department of Computer ScienceUniversity of FreiburgGermany
  3. 3.Department of Computer ScienceGeorgetown UniversityUSA

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