Immune Size Approximation Algorithms in Ad Hoc Radio Network

  • Marek Klonowski
  • Kamil Wolny
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7158)


In this paper we discuss size approximation protocols in a single hop radio network with an adversary that aims at changing the result of the protocol, controlling some stations in the network. As a first contribution we show that most of known size approximation procedures discussed in the literature can be attacked by the adversary with very limited resources (i.e significantly less than regular stations). This is an introduction for the main contribution of this paper - we present an efficient size approximation protocol immune against adversary able to control moderate number of stations.


Radio Network Size Approximation Collision Detection Local Estimator Pseudo Random Number Generator 
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.


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  1. 1.
    Bar-Yehuda, R., Goldreich, O., Itai, A.: Efficient emulation of single-hop radio network with collision detection on multi-hop radio network with no collision detection. Distributed Computing 5, 67–71 (1991)CrossRefzbMATHGoogle Scholar
  2. 2.
    Bordim, J.L., Cui, J.T., Ishii, N., Nakano, K.: Doubly-logarithmic energy-efficient initialization protocols for single-hop radio networks. In: IPDPS. IEEE Computer Society (2002)Google Scholar
  3. 3.
    Chernoff, H.: A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Ann. Math. Stat. 23, 493–507 (1952)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Dahmen, E., Krauß, C.: Short Hash-Based Signatures for Wireless Sensor Networks. In: Garay, J.A., Miyaji, A., Otsuka, A. (eds.) CANS 2009. LNCS, vol. 5888, pp. 463–476. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Flajolet, P., Sedgewick, R.: Mellin transforms and asymptotics: Finite differences and rice’s integrals. Theoretical Computer Science 144, 101–124 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Greenberg, A.G., Flajolet, P., Ladner, R.E.: Estimating the multiplicities of conflicts to speed their resolution in multiple access channels. J. ACM 34(2), 289–325 (1987)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Hofri, M.: A feedback-less distributed broadcast algorithm for multihop radio networks with time-varying structure. In: Iazeolla, G., Courtois, P.-J., Boxma, O.J. (eds.) Computer Performance and Reliability, pp. 353–368. North-Holland (1987)Google Scholar
  8. 8.
    Jurdzinski, T., Kutylowski, M., Zatopianski, J.: Efficient algorithms for leader election in radio networks. In: PODC, pp. 51–57 (2002)Google Scholar
  9. 9.
    Jurdziński, T., Kutyłowski, M., Zatopianski, J.: Energy-Efficient Size Approximation of Radio Networks with No Collision Detection. In: Ibarra, O.H., Zhang, L. (eds.) COCOON 2002. LNCS, vol. 2387, pp. 279–289. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Kabarowski, J., Kutyłowski, M., Rutkowski, W.: Adversary Immune Size Approximation of Single-Hop Radio Networks. In: Cai, J.-Y., Cooper, S.B., Li, A. (eds.) TAMC 2006. LNCS, vol. 3959, pp. 148–158. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Kutyłowski, J., Zagórski, F.: Reliable Broadcasting Without Collision Detection. In: Wiedermann, J., Tel, G., Pokorný, J., Bieliková, M., Štuller, J. (eds.) SOFSEM 2006. LNCS, vol. 3831, pp. 389–398. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Kutyłowski, M., Rutkowski, W.: Adversary Immune Leader Election in ad hoc Radio Networks. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 397–408. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Merkle, R.C.: A Digital Signature Based on a Conventional Encryption Function. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 369–378. Springer, Heidelberg (1988)Google Scholar
  14. 14.
    Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press (1995)Google Scholar
  15. 15.
    Szpankowski, W., Rego, V.: Yet another application of a binomial recurrence. order statistics 43, 401–410 (1990)zbMATHMathSciNetGoogle Scholar
  16. 16.
    Weisstein, E.W.: Weisstein, eric w. ”exponential integral.” from mathworld–a wolfram web resource,
  17. 17.
    Weisstein, E.W.: Weisstein, eric w. ”shi.” from mathworld–a wolfram web resource,
  18. 18.
    Willard, D.E.: Log-logarithmic selection resolution protocols in a multiple access channel. SIAM J. Comput. 15(2), 468–477 (1986)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Marek Klonowski
    • 1
  • Kamil Wolny
    • 1
  1. 1.Wrocław University of TechnologyPoland

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