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Broadcasting in UDG radio networks with unknown topology

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Abstract

The paper considers broadcasting in radio networks, modeled as unit disk graphs (UDG). Such networks occur in wireless communication between sites (e.g., stations or sensors) situated in a terrain. Network stations are represented by points in the Euclidean plane, where a station is connected to all stations at distance at most 1 from it. A message transmitted by a station reaches all its neighbors, but a station hears a message (receives the message correctly) only if exactly one of its neighbors transmits at a given time step. One station of the network, called the source, has a message which has to be disseminated to all other stations. Stations are unaware of the network topology. Two broadcasting models are considered. In the conditional wake up model, the stations other than the source are initially idle and cannot transmit until they hear a message for the first time. In the spontaneous wake up model, all stations are awake (and may transmit messages) from the beginning. It turns out that broadcasting time depends on two parameters of the UDG network, namely, its diameter D and its granularity g, which is the inverse of the minimum distance between any two stations. We present a deterministic broadcasting algorithm which works in time O (D g) under the conditional wake up model and prove that broadcasting in this model cannot be accomplished by any deterministic algorithm in time better than \({\Omega (D \sqrt{g})}\) . For the spontaneous wake up model, we design two deterministic broadcasting algorithms: the first works in time O (D + g 2) and the second in time O (D log g). While neither of these algorithms alone is optimal for all parameter values, we prove that the algorithm obtained by interleaving their steps, and thus working in time \({ O \left( \min\left\{ D + g^2, D \log{g}\right\}\right) }\), turns out to be optimal by establishing a matching lower bound.

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References

  1. Alon N., Bar-Noy A., Linial N., Peleg D.: A lower bound for radio broadcast. J. Comp. Syst. Sci. 43, 290–298 (1991)

    Article  MathSciNet  Google Scholar 

  2. Avin, C., Ercal, G.: On the cover time of random geometric graphs. In: Proc. 32th Int. Colloq. on Automata, Languages and Programming (ICALP 2005). LNCS, vol. 3580, pp. 677–689 (2005)

  3. Bar-Yehuda R., Goldreich O., Itai A.: On the time complexity of broadcast in radio networks: an exponential gap between determinism and randomization. J. Comp. Syst. Sci. 45, 104–126 (1992)

    Article  MathSciNet  Google Scholar 

  4. Bruschi D., Del Pinto M.: Lower bounds for the broadcast problem in mobile radio networks. Distributed Comput. 10, 129–135 (1997)

    Article  Google Scholar 

  5. Chlamtac I., Kutten S.: On broadcasting in radio networks—problem analysis and protocol design. IEEE Trans. Commun. 33, 1240–1246 (1985)

    Article  Google Scholar 

  6. Chlamtac I., Weinstein O.: The wave expansion approach to broadcasting in multihop radio networks. IEEE Trans. Commun. 39, 426–433 (1991)

    Article  Google Scholar 

  7. Chlebus B., Ga̧sieniec L., Gibbons A., Pelc A., Rytter W.: Deterministic broadcasting in unknown radio networks. Distributed Comput. 15, 27–38 (2002)

    Article  Google Scholar 

  8. Chlebus, B., Ga̧sieniec, L., Östlin, A., Robson, J.M.: Deterministic radio broadcasting. In: Proc. 27th Int. Colloq. on Automata, Languages and Programming (ICALP 2000). LNCS, vol. 1853, pp. 717–728 (2000)

  9. Chlebus, B., Kowalski, D.: A better wake-up in radio networks. In: Proc. 23rd Symp. on Principles of Distributed Computing (PODC 2004) (2004)

  10. Chrobak, M., Ga̧sieniec, L., Kowalski, D.: The wake-up problem in multi-hop radio networks. In: Proc. 15th ACM-SIAM Symp. on Discrete Algorithms (SODA 2004), pp. 985–993 (2004)

  11. Chrobak, M., Ga̧sieniec, L., Rytter, W.: Fast broadcasting and gossiping in radio networks. In: Proc. 41st Symp. on Foundations of Computer Science (FOCS 2000), pp. 575–581 (2000)

  12. Clementi, A.E.F., Monti, A., Silvestri, R.: Selective families, superimposed codes, and broadcasting on unknown radio networks. In: Proc. 12th Ann. ACM-SIAM Symp. on Discrete Algorithms (SODA 2001), pp. 709–718 (2001)

  13. Czumaj, A., Rytter, W.: Broadcasting algorithms in radio networks with unknown topology. In: Proc. 44th Symp. on Foundations of Computer Science (FOCS 2003), pp. 492–501 (2003)

  14. De Marco, G.: Distributed broadcast in unknown radio networks. In: Proc. 19th ACM-SIAM Symp. on Discrete Algorithms (SODA 2008) (2008)

  15. Dessmark A., Pelc A.: Broadcasting in geometric radio networks. J. Discrete Algorithms 5, 187–201 (2007)

    Article  MathSciNet  Google Scholar 

  16. Diks K., Kranakis E., Krizanc D., Pelc A.: The impact of knowledge on broadcasting time in linear radio networks. Theor. Comp. Sci. 287, 449–471 (2002)

    Article  Google Scholar 

  17. Elkin, M., Kortsarz, G.: Improved broadcast schedule for radio networks. In: Proc. 16th ACM-SIAM Symp. on Discrete Algorithms (SODA 2005), pp. 222–231 (2005)

  18. Emek, Y., Kantor, E., Peleg, D.: On the effect of the deployment setting on broadcasting in Euclidean radio networks (submitted)

  19. Fusco, E., Pelc, A.: Broadcasting in UDG radio networks with missing and inaccurate information (submitted)

  20. Gaber I., Mansour Y.: Centralized broadcast in multihop radio networks. J. Algorithms 46, 1–20 (2003)

    Article  MathSciNet  Google Scholar 

  21. Ga̧sieniec L., Pelc A., Peleg D.: The wakeup problem in synchronous broadcast systems. SIAM J. Discrete Math. 14, 207–222 (2001)

    Article  MathSciNet  Google Scholar 

  22. Ga̧sieniec, L., Peleg, D., Xin, Q.: Faster communication in known topology radio networks. In: Proc. 24th ACM Symp. on Principles Of Distributed Computing (PODC 2005), pp. 129–137 (2005)

  23. Jurdzinski, T., Stachowiak, G.: Probabilistic algorithms for the wakeup problem in single-hop radio networks. In: Proc. 13th Int. Symp. on Algorithms and Computation (ISAAC 2002). LNCS, vol. 2518, pp. 535–549 (2002)

  24. Kesselman, A., Kowalski, D.: Fast Distributed Algorithm for Convergecast in Ad Hoc Geometric Radio Networks. In: Proc. 2nd Int. Conf. on Wireless on Demand Network Systems and Service (WONS 2005), pp. 119–124 (2005)

  25. Kowalski D., Pelc A.: Time of deterministic broadcasting in radio networks with local knowledge. SIAM J. Comput. 33, 870–891 (2004)

    Article  MathSciNet  Google Scholar 

  26. Kowalski D., Pelc A.: Time complexity of radio broadcasting: adaptiveness vs. obliviousness and randomization vs. determinism. Theor. Comp. Sci. 333, 355–371 (2005)

    Article  MathSciNet  Google Scholar 

  27. Kowalski D., Pelc A.: Broadcasting in undirected ad hoc radio networks. Distributed Comput. 18, 43–57 (2005)

    Article  Google Scholar 

  28. Kowalski D., Pelc A.: Optimal deterministic broadcasting in known topology radio networks. Distributed Comput. 19, 185–195 (2007)

    Article  Google Scholar 

  29. Kranakis E., Krizanc D., Pelc A.: Fault-tolerant broadcasting in radio networks. J. Algorithms 39, 47–67 (2001)

    Article  MathSciNet  Google Scholar 

  30. Kuhn, F., Zollinger, A.: Ad-hoc networks beyond unit disk graphs. In: Proc. DIALM-POMC Joint Workshop on Foundations of Mobile Computing, pp. 69–78 (2003)

  31. Kushilevitz E., Mansour Y.: An Ω(D log (N/D)) lower bound for broadcast in radio networks. SIAM J. Comput. 27, 702–712 (1998)

    Article  MathSciNet  Google Scholar 

  32. Moscibroda, T., Wattenhofer, R.: Maximal independent sets in radio networks. In: Proc. 24th ACM Symp. on Principles of Distributed Computing (PODC 2005), pp. 148–157 (2005)

  33. Moscibroda, T., Wattenhofer, R.: Coloring unstructured radio networks. In: Proc. 17th ACM Symp. on Parallel Algorithms (SPAA 2005), pp. 39–48 (2005)

  34. Muthukrishnan, S., Pandurangan, G.: The bin-covering technique for thresholding random geometric graph properties. In: Proc. 16th ACM-SIAM Symp. on Discrete Algorithms (SODA 2005), pp. 989–998 (2005)

  35. Ravishankar K., Singh S.: Broadcasting on [0,L]. Discrete Appl. Math. 53, 299–319 (1994)

    Article  MathSciNet  Google Scholar 

  36. Sen, A., Huson, M. L.: A New Model for Scheduling Packet Radio Networks. In: Proc. 15th Joint Conf. of the IEEE Computer and Communication Societies (IEEE INFOCOM 1996), pp. 1116–1124 (1996)

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Authors and Affiliations

  1. School of Electrical Engineering, Tel Aviv University, Tel Aviv, 69978, Israel

    Yuval Emek

  2. Department of Computer Science, University of Liverpool, Liverpool, L69 3BX, UK

    Leszek Ga̧sieniec & Chang Su

  3. Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science, Rehovot, 76100, Israel

    Erez Kantor & David Peleg

  4. Département d’informatique, Université du Québec en Outaouais, Gatineau, QC, J8X 3X7, Canada

    Andrzej Pelc

Authors
  1. Yuval Emek
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  2. Leszek Ga̧sieniec
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  3. Erez Kantor
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  4. Andrzej Pelc
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  5. David Peleg
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  6. Chang Su
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Correspondence to Yuval Emek.

Additional information

The research of Leszek Ga̧sieniec is partially supported by Royal Society International Joint Project 2006/R2. The research of Andrzej Pelc is partially supported by NSERC discovery grant and by the Research Chair in Distributed Computing at the Université du Québec en Outaouais. The research of David Peleg is partially supported by grants from the Minerva Foundation and the Israel Ministry of Science.

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Emek, Y., Ga̧sieniec, L., Kantor, E. et al. Broadcasting in UDG radio networks with unknown topology. Distrib. Comput. 21, 331–351 (2009). https://doi.org/10.1007/s00446-008-0075-z

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  • DOI: https://doi.org/10.1007/s00446-008-0075-z

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