Advertisement

Algorithmica

, Volume 54, Issue 1, pp 118–139 | Cite as

Many-to-Many Communication in Radio Networks

  • Bogdan S. ChlebusEmail author
  • Dariusz R. Kowalski
  • Tomasz Radzik
Article

Abstract

Radio networks model wireless data communication when the bandwidth is limited to one wave frequency. The key restriction of such networks is mutual interference of packets arriving simultaneously at a node. The many-to-many (m2m) communication primitive involves p participant nodes from among n nodes in the network, where the distance between any pair of participants is at most d. The task is to have all the participants get to know all the input messages. We consider three cases of the m2m communication problem. In the ad-hoc case, each participant knows only its name and the values of n, p and d. In the partially centralized case, each participant knows the topology of the network and the values of p and d, but does not know the names of the other participants. In the centralized case, each participant knows the topology of the network and the names of all the participants. For the centralized m2m problem, we give deterministic protocols, for both undirected and directed networks, working in \({\mathcal{O}}(d+p)\) time, which is provably optimal. For the partially centralized m2m problem, we give a randomized protocol for undirected networks working in \({\mathcal{O}}((d+p+\log^{2}n)\log p)\) time with high probability (whp), and we show that any deterministic protocol requires \(\Omega(d+p\frac{\log n}{\log p})\) time. For the ad-hoc m2m problem, we develop a randomized protocol for undirected networks that works in \({\mathcal{O}}((d+\log p)\log^{2}n+p\log p)\) time whp. We show two lower bounds for the ad-hoc m2m problem. One lower bound states that any randomized protocol for the m2m ad hoc problem requires \(\Omega(p+d\log\frac{n}{d})\) expected time. Another lower bound states that for any deterministic protocol for the m2m ad hoc problem, there is a network on which the protocol requires \(\Omega(n\frac{\log n}{\log(n/d)})\) time when np(n)=Ω(n) and d>1, and that it requires Ω(n) time when np(n)=o(n).

Keywords

Radio network Many-to-many communication Broadcast Gossiping Centralized protocol Distributed protocol Randomization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alon, N., Bar-Noy, A., Linial, N., Peleg, D.: A lower bound for radio broadcast. J. Comput. Syst. Sci. 43, 290–298 (1991) zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bar-Yehuda, R., Goldreich, O., Itai, A.: On the time complexity of broadcast in radio networks: an exponential gap between determinism and randomization. J. Comput. Syst. Sci. 45, 104–126 (1992) zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bar-Yehuda, R., Israeli, A., Itai, A.: Multiple communication in multihop radio networks. SIAM J. Comput. 22, 875–887 (1993) zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Chlamtac, I., Kutten, S.: On broadcasting in radio networks—problem analysis and protocol design. IEEE Trans. Commun. 33, 1240–1246 (1985) zbMATHCrossRefGoogle Scholar
  5. 5.
    Chlamtac, I., Weinstein, O.: The wave expansion approach to broadcasting in multihop radio networks. IEEE Trans. Commun. 39, 426–433 (1991) CrossRefGoogle Scholar
  6. 6.
    Chlebus, B.S., Rokicki, M.R.: Centralized asynchronous broadcast in radio networks. Theor. Comput. Sci. 383, 5–22 (2007) zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Chlebus, B.S., Gąsieniec, L., Östlin, A., Robson, J.M.: Deterministic radio broadcasting. In: Proceedings, 27th Colloquium on Automata, Languages and Programming (ICALP). LNCS, vol. 1853, pp. 717–728 (2000) Google Scholar
  8. 8.
    Chlebus, B.S., Gąsieniec, L., Gibbons, A., Pelc, A., Rytter, W.: Deterministic broadcasting in unknown radio networks. Distrib. Comput. 15, 27–38 (2002) CrossRefGoogle Scholar
  9. 9.
    Chlebus, B.S., Gąsieniec, L., Kowalski, D.R., Radzik, T.: On the wake-up problem in radio networks. In: Proceedings, 32nd Colloquium on Automata, Languages and Programming (ICALP). LNCS, vol. 3580, pp. 347–359 (2005) Google Scholar
  10. 10.
    Chlebus, B.S., Kowalski, D.R., Rokicki, M.R.: Average-time complexity of gossiping in radio networks. In: Proceedings, 13th Colloquium on Structural Information and Communication Complexity (SIROCCO). LNCS, vol. 4056, pp. 253–26 (2006) Google Scholar
  11. 11.
    Clementi, A.E.F., Crescenzi, P., Monti, A., Penna, P., Silvestri, R.: On computing ad-hoc selective families. In: Proceedings, 5th Workshop on Randomization and Approximation Techniques in Computer Science (APPROX-RANDOM). LNCS, vol. 2129, pp. 211–222 (2001) Google Scholar
  12. 12.
    Clementi, A.E.F., Monti, A., Silvestri, R.: Distributed broadcast in radio networks of unknown topology. Theor. Comput. Sci. 302, 337–364 (2003) zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Czumaj, A., Rytter, W.: Broadcasting algorithms in radio networks with unknown topology. J. Algorithms 60, 115–143 (2006) zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Elkin, M., Kortsarz, G.: A logarithmic lower bound for radio broadcast. J. Algorithms 52, 8–25 (2004) zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Elkin, M., Kortsarz, G.: Polylogarithmic additive inapproximability of the radio broadcast problem. SIAM J. Discrete Math. 19, 881–899 (2005) zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Elkin, M., Kortsarz, G.: An improved algorithm for radio broadcast. ACM Trans. Algorithms 3 (2007) Google Scholar
  17. 17.
    Gaber, I., Mansour, Y.: Centralized broadcast in multihop radio networks. J. Algorithms 46, 1–20 (2003) zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Gąsieniec, L., Potapov, I.: Gossiping with unit messages in known radio networks. In: Proceedings, 2nd IFIP Conference on Theoretical Computer Science (TCS), pp. 193–205 (2002) Google Scholar
  19. 19.
    Gąsieniec, L., Pelc, A., Peleg, D.: The wakeup problem in synchronous broadcast systems. SIAM J. Discrete Math. 14, 207–222 (2001) zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Gąsieniec, L., Pagourtzis, A., Potapov, I.: Deterministic communication in radio networks with large labels. In: Proceedings, 10th European Symposium on Algorithms (ESA). LNCS, vol. 2461, pp. 512–524 (2002) Google Scholar
  21. 21.
    Gąsieniec, L., Potapov, I., Xin, Q.: Time efficient gossiping in known radio networks. In: Proceedings, 11th Colloquium on Structural Information and Communication Complexity (SIROCCO). LNCS, vol. 3104, pp. 173–184 (2004) Google Scholar
  22. 22.
    Gąsieniec, L., Radzik, T., Xin, Q.: Faster deterministic gossiping in directed ad-hoc radio networks. In: Proceedings, 9th Scandinavian Workshop on Algorithm Theory (SWAT). LNCS, vol. 3111, pp. 397–407 (2004) Google Scholar
  23. 23.
    Gąsieniec, L., Peleg, D., Xin, Q.: Faster communication in known topology radio networks. In: Proceedings, 24th ACM Symposium on Principles of Distributed Computing (PODC), pp. 129–137 (2005) Google Scholar
  24. 24.
    Gąsieniec, L., Kranakis, E., Pelc, A., Xin, Q.: Deterministic M2M multicast in radio networks. Theor. Comput. Sci. 362, 196–206 (2006) zbMATHCrossRefGoogle Scholar
  25. 25.
    Greenberg, A.G., Winograd, S.: A lower bound on the time needed in the worst case to resolve conflicts deterministically in multiple access channels. J. ACM 32, 589–596 (1985) zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Indyk, P.: Explicit constructions of selectors and related combinatorial structures, with applications. In: Proceedings, 13th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 697–704 (2002) Google Scholar
  27. 27.
    Kowalski, D.R., Pelc, A.: Time of deterministic broadcasting in radio networks with local knowledge. SIAM J. Comput. 33, 870–891 (2004) zbMATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    Kowalski, D.R., Pelc, A.: Broadcasting in undirected ad hoc radio networks. Distrib. Comput. 18, 43–57 (2005) CrossRefGoogle Scholar
  29. 29.
    Kowalski, D.R., Pelc, A.: Optimal deterministic broadcasting in known topology radio networks. Distrib. Comput. 19, 185–195 (2007) CrossRefGoogle Scholar
  30. 30.
    Kushilevitz, E., Mansour, Y.: An Ω(Dlog (N/D)) lower bound for broadcast in radio networks. SIAM J. Comput. 27, 702–712 (1998) zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Bogdan S. Chlebus
    • 1
    Email author
  • Dariusz R. Kowalski
    • 2
  • Tomasz Radzik
    • 3
  1. 1.Department of Computer Science and EngineeringUniversity of Colorado DenverDenverUSA
  2. 2.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK
  3. 3.Department of Computer ScienceKing’s College LondonLondonUK

Personalised recommendations