Energy-Efficient Size Approximation of Radio Networks with No Collision Detection

  • Tomasz Jurdziński
  • Mirosław Kutyłowski
  • Jan Zatopiański
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2387)

Abstract

Algorithms for radio networks are studied in two scenarios: (a) the number of active stations is known (or approximately known) (b) the number of active stations is unknown. In the second (more realistic) case it is much harder to design efficient algorithms. For this reason, we design an efficient randomized algorithm for a single-hop radio network that approximately counts the number of its active stations. With probability higher than 1 - 1/n, this approximation is within a constant factor, the algorithm runs in poly-logarithmic time and its energy cost is o(loglogn). This improves the previous O(logn) bound for energy. In particular, our algorithm can be applied to improve energy cost of known leader election and initialization protocols (without loss of time efficiency).

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References

  1. 1.
    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 Systems Sciences 45(1) (1992), 104–126MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bordim, J.L., Cui, J., Hayashi, T., Nakano, K., Olariu, S.: Energy-Efficient Initialization Protocols for Ad-hoc Radio Networks. ISAAC’99, LNCS 741, Springer-Verlag, 1999, 215–224Google Scholar
  3. 3.
    Chlebus, B.S.: Randomized Communication in Radio Networks. A chapter in „Handbook on Randomized Computing” P. M. Pardalos, S. Rajasekaran, J. H. Reif, J. D. P. Rolim, (Eds.), Kluwer Academic Publishers, to appearGoogle Scholar
  4. 4.
    Chlamtac, I., Kutten, S.: On Broadcasting in Radio Networks-Problem Analysis and Protocol Design. IEEE Trans. on Commun. 33 (1985), 1240–1246MATHCrossRefGoogle Scholar
  5. 5.
    Dessmark, A., Pelc, A.: Deterministic Radio Broadcasting at Low Cost. STACS’2001, LNCS 2010, Springer-Verlag, 158–169Google Scholar
  6. 6.
    Fifer, W.C., Bruno, F.J.: Low Cost Packet Radio. Proc. of the IEEE 75 (1987), 33–42CrossRefGoogle Scholar
  7. 7.
    Gçsieniec, L., Pelc, A., Peleg, D.: The Wakeup Problem in Synchronous Broadcast Systems. SIAM Journal on Discrete Math. 14(2) (2001), 207–222CrossRefGoogle Scholar
  8. 8.
    Gçsieniec, L., Lingas, A.: On Adaptive Deterministic Gossiping in Ad Hoc Radio Networks. ACM-SIAM SODA’ 2002Google Scholar
  9. 9.
    Gitman, I., Van Slyke, R.M., Frank, H.: Routing in Packet-Switching Broadcast Radio Networks. IEEE Trans. on Commun. COM-24 (1976), 926–930CrossRefGoogle Scholar
  10. 10.
    Hayashi, T., Nakano, K., Olariu, S.: Randomized Initialization Protocols for Packet Radio Networks. IPPS’1999, IEEE 1999, 544–548Google Scholar
  11. 11.
    Jurdziński, T., Kutyłowski, M., Zatopiański, J.: Weak Communication in Radio Networks. Euro-Par’2002, LNCS, Springer-Verlag (accepted paper)Google Scholar
  12. 12.
    Jurdziński, T., Kutyłowski, M., Zatopiański, J.: Efficient Algorithms for Leader Election in Radio Networks. ACM PODC’2002, (accepted paper)Google Scholar
  13. 13.
    Jurdziński, T., Kutyłowski, M., Zatopiański, J.: Energy-Efficient Size Approximation for Radio Networks with no Collision Detection. Technical Report CSR-02-02, Technische Universität Chemnitz, Fakultät für Informatik, http://www.tu-chemnitz.de/informatik/
  14. 14.
    Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press, 1995Google Scholar
  15. 15.
    Nakano, K., Olariu, S.: Randomized Leader Election Protocols in Radio Networks with No Collision Detection. ISAAC’2000, LNCS 1969, Springer-Verlag, 362–373Google Scholar
  16. 16.
    Nakano, K., Olariu, S.: Energy Efficient Initialization Protocols for Radio Networks with no Collision Detection. ICPP’2000, IEEE 2000, 263–270Google Scholar
  17. 17.
    Nakano, K., Olariu, S.: Energy-Efficient Randomized Routing in Radio Networks. Proc. of 4th Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications (DIALM), 35–44Google Scholar
  18. 18.
    Salkintzis, A.K., Chamzas, C.: An In-band Power-saving Protocol for Mobile Data Networks. IEEE Trans. on Communication, COM-46 (1998), 1194-1205Google Scholar
  19. 19.
    Willard, D.E.: Log-logarithmic Selection Resolution Protocols in Multiple Access Channel. SIAM Journal on Computing 15 (1986), 468–477MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Tomasz Jurdziński
    • 1
    • 2
  • Mirosław Kutyłowski
    • 3
  • Jan Zatopiański
    • 2
  1. 1.Institute of Computer ScienceTechnical University ChemnitzUSA
  2. 2.Institute of Computer ScienceWrocław UniversityUSA
  3. 3.Institute of MathematicsWrocław University of TechnologyUSA

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