Abstract
We study the communication primitives of broadcasting (one-to-all communication) and gossiping (all-to-all communication) in known topology radio networks, i.e., where for each primitive the schedule of transmissions is precomputed based on full knowledge about the size and the topology of the network. We show that gossiping can be completed in \(O(D+\frac{\varDelta\log n}{\log{\varDelta}-\log{\log n}})\) time units in any radio network of size n, diameter D, and maximum degree Δ=Ω(log n). This is an almost optimal schedule in the sense that there exists a radio network topology, specifically a Δ-regular tree, in which the radio gossiping cannot be completed in less than \(\varOmega(D+\frac{\varDelta\log n}{\log{\varDelta}})\) units of time. Moreover, we show a \(D+O(\frac{\log^{3}n}{\log{\log n}})\) schedule for the broadcast task. Both our transmission schemes significantly improve upon the currently best known schedules by Gąsieniec, Peleg, and Xin (Proceedings of the 24th Annual ACM SIGACT-SIGOPS PODC, pp. 129–137, 2005), i.e., a O(D+Δlog n) time schedule for gossiping and a D+O(log 3 n) time schedule for broadcast. Our broadcasting schedule also improves, for large D, a very recent O(D+log 2 n) time broadcasting schedule by Kowalski and Pelc.
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References
Alon, N., Bar-Noy, A., Linial, N., Peleg, D.: A lower bound for radio broadcast. J. Comput. Syst. Sci. 43, 290–298 (1991)
Chlamtac, I., Kutten, S.: On broadcasting in radio networks-problem analysis and protocol design. IEEE Trans. Commun. 33, 1240–1246 (1985)
Chlamtac, I., Weinstein, O.: The wave expansion approach to broadcasting in multihop radio networks. IEEE Trans. Commun. 39, 426–433 (1991)
Diks, K., Kranakis, E., Krizanc, D., Pelc, A.: The impact of information on broadcasting time in linear radio networks. Theor. Comput. Sci. 287, 449–471 (2002)
Elkin, M., Kortsarz, G.: Improved broadcast schedule for radio networks. In: Proceedings of the 16th ACM-SIAM Symposium on Discrete Algorithms, pp. 222–231 (2005)
Gaber, I., Mansour, Y.: Broadcast in radio networks. In: Proceedings of the 6th ACM-SIAM Symposium on Discrete Algorithms, pp. 577–585 (1995)
Gąsieniec, L., Peleg, D., Xin, Q.: Faster communication in known topology radio networks. In: Proceedings of the 24th Annual ACM SIGACT-SIGOPS PODC, pp. 129–137 (2005)
Gąsieniec, L., Potapov, I.: Gossiping with unit messages in known radio networks. In: Proceedings of the 2nd IFIP International Conference on Theoretical Computer Science, pp. 193–205 (2002)
Gąsieniec, L., Potapov, I., Xin, Q.: Efficient gossiping in known radio networks. In: Proceedings of the 11th SIROCCO. Lecture Notes in Computer Science, vol. 3104, pp. 173–184. Springer, Berlin (2004)
Kowalski, D., Pelc, A.: Optimal deterministic broadcasting in known topology radio networks. Distributed Comput. 19(3), 185–195 (2007)
Manne, F., Wang, S., Xin, Q.: Faster radio broadcast in planar graphs. In: Proceedings of the 4th Conference on Wireless on Demand Network Systems and Services. pp. 9–13. IEEE Press (2007)
Manne, F., Xin, Q.: Optimal gossiping with unit size messages in known topology radio networks. In: Proceedings of the 3rd Workshop on Combinatorial and Algorithmic Aspects of Networking. Lecture Notes in Computer Science, vol. 4235, pp. 125–134. Springer, Berlin (2006)
Sen, A., Huson, M.L.: A new model for scheduling packet radio networks. In: Proceedings of the 15th Joint Conference of IEEE Computer and Communication Societies, pp. 1116–1124 (1996)
Strahler, A.N.: Hypsometric (area-altitude) analysis of erosional topology. Bull. Geol. Soc. Am. 63, 117–1142 (1952)
Viennot, X.G.: A Strahler bijection between Dyck paths and planar trees. Discrete Math. 246, 317–329 (2002)
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A preliminary version of this paper appeared in the proceedings of ISAAC’06.
F. Cicalese supported by the Sofja Kovalevskaja Award 2004 of the Alexander von Humboldt Stiftung. F. Manne and Q. Xin supported by the Research Council of Norway through the SPECTRUM project.
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Cicalese, F., Manne, F. & Xin, Q. Faster Deterministic Communication in Radio Networks. Algorithmica 54, 226–242 (2009). https://doi.org/10.1007/s00453-007-9136-0
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DOI: https://doi.org/10.1007/s00453-007-9136-0