On the Complexity of Distributed Broadcasting and MDS Construction in Radio Networks

  • Tomasz Jurdzinski
  • Dariusz R. Kowalski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7702)


We study two fundamental problems in the model of undirected radio networks: broadcasting and construction of a Minimal Dominating Set (MDS). The network is ad hoc, in the sense that initially nodes know only their own ID and the IDs of their neighbors. For both problems, we provide deterministic distributed algorithms working in \(O(D\sqrt{n} \log^6 n)\) communication rounds, and complement them by a close lower bound \(\Omega(\sqrt{Dn\log(n/D)})\), where n is the number of nodes and D is the radius of the radio network. Our work provides several novel algorithmic methods for overcoming the impact of collisions in radio networks, and shrinks the gap between the lower and the upper bounds for the considered problems from polynomial to polylogarithmic, for networks with small (polylogarithmic) radius.


radio networks broadcasting minimal dominating set distributed algorithms 


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  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. J. Comput. Syst. Sci. 45(1), 104–126 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    De Bonis, A., Gąsieniec, L., Vaccaro, U.: Generalized Framework for Selectors With Applications in Optimal Group Testing. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 81–96. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  3. 3.
    Brito, C.F., Vaya, S.: Improved lower bound for deterministic broadcasting in radio networks. Theor. Comput. Sci. 412(29), 3568–3578 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Chlamtac, I., Kutten, S.: Tree-based broadcasting in multihop radio networks. IEEE Trans. Computers 36(10), 1209–1223 (1987)CrossRefGoogle Scholar
  5. 5.
    Chlamtac, I., Weinstein, O.: The wave expansion approach to broadcasting in multihop radio networks. IEEE Transactions on Communications 39(3), 426–433 (1991)CrossRefGoogle Scholar
  6. 6.
    Chlebus, B.S., Kowalski, D.R.: Almost Optimal Explicit Selectors. In: Liśkiewicz, M., Reischuk, R. (eds.) FCT 2005. LNCS, vol. 3623, pp. 270–280. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Clementi, A.E.F., Monti, A., Silvestri, R.: Selective families, superimposed codes, and broadcasting on unknown radio networks. In: SODA, pp. 709–718 (2001)Google Scholar
  8. 8.
    Czumaj, A., Rytter, W.: Broadcasting algorithms in radio networks with unknown topology. J. Algorithms 60(2), 115–143 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Goldberg, L.A., Jerrum, M., Leighton, F.T., Rao, S.: Doubly logarithmic communication algorithms for optical-communication parallel computers. SIAM J. Comput. 26(4), 1100–1119 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Kowalski, D.R., Pelc, A.: Time of deterministic broadcasting in radio networks with local knowledge. SIAM J. Comput. 33(4), 870–891 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Kowalski, D.R., Pelc, A.: Broadcasting in undirected ad hoc radio networks. Distributed Computing 18(1), 43–57 (2005)CrossRefGoogle Scholar
  12. 12.
    Kushilevitz, E., Mansour, Y.: An omega(d log (n/d)) lower bound for broadcast in radio networks. SIAM J. Comput. 27(3), 702–712 (1998)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Tomasz Jurdzinski
    • 1
  • Dariusz R. Kowalski
    • 2
  1. 1.Institute of Computer ScienceUniversity of WrocławPoland
  2. 2.Department of Computer ScienceUniversity of LiverpoolUnited Kingdom

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