Abstract
We show new lower bounds for collision-free transmissions in Radio Networks. Our main result is a tight lower bound of Ω(log n log (1/ε)) on the time required by a uniform randomized protocol to achieve a clear transmission with success probability 1–ε in a one-hop setting. This result is extended to non-uniform protocols as well. A new lower bound is proved for the important multi-hop setting of nodes distributed as a connected Random Geometric Graph. Our main result is tight for a variety of problems.
This research was supported in part by DIMACS, Center for Discrete Mathematics & Theoretical Computer Science, grants numbered NSF CCR 00-87022, NSF EIA 02-05116 and Alfred P. Sloan Foundation 99-10-8.
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References
Farach-Colton, M., Fernandes, R.J., Mosteiro, M.A.: Bootstrapping a hop-optimal network in the weak sensor model. In: Proc. of the 13th Annual European Symposium on Algorithms (2005)
Gasieniec, L., Pelc, A., Peleg, D.: The wakeup problem in synchronous broadcast systems. In: Proceedings 19th Annual ACM Symposium on Principles of Distributed Computing (2000)
Hayashi, T., Nakano, K., Olariu, S.: Randomized initialization protocols packet radio networks. In: IPPS (1999)
Jurdziński, T., Stachowiak, G.: Probabilistic algorithms for the wakeup problem in singlehop radio networks. In: Bose, P., Morin, P. (eds.) ISAAC 2002. LNCS, vol. 2518, pp. 535–549. Springer, Heidelberg (2002)
Kushilevitz, E., Mansour, Y.: An Ω(Dlog(N/D)) lower bound for broadcast in radio networks. SIAM J. Comput. 27(3), 702–712 (1998)
Mitrinović, D.S.: Elementary Inequalities. P. Noordhoff Ltd., Groningen (1964)
Moscibroda, T., Wattenhofer, R.: Maximal independent sets in radio networks. In: PODC (2005)
Muthukrishnan, S., Pandurangan, G.: The bin-covering technique for thresholding random geometric graph properties. In: Proc. of ACM-SODA (2005)
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© 2006 Springer-Verlag Berlin Heidelberg
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Farach-Colton, M., Fernandes, R.J., Mosteiro, M.A. (2006). Lower Bounds for Clear Transmissions in Radio Networks. In: Correa, J.R., Hevia, A., Kiwi, M. (eds) LATIN 2006: Theoretical Informatics. LATIN 2006. Lecture Notes in Computer Science, vol 3887. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11682462_42
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DOI: https://doi.org/10.1007/11682462_42
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