Abstract
The paper considers broadcasting protocols in radio networks with known topology that are efficient in both time and energy. The radio network is modelled as an undirected graph G = (V, E) where |V| = n. It is assumed that during execution of the communication task every node in V is allowed to transmit at most once. Under this assumption it is shown that any radio broadcast protocol requires \({D+\Omega(\sqrt{n-D})}\) transmission rounds, where D is the diameter of G. This lower bound is complemented with an efficient construction of a deterministic protocol that accomplishes broadcasting in \({D+O(\sqrt{n}\log n)}\) rounds. Moreover, if we allow each node to transmit at most k times, the lower bound \({D+\Omega((n-D)^{1/(2k)})}\) on the number of transmission rounds holds. We also provide a randomised protocol that accomplishes broadcasting in \({D+O(kn^{1/(k-2)}\log^2 n)}\) rounds. The paper concludes with a number of open problems in the area.
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The research of L. Gąsieniec, D.R. Kowalski and C. Su supported in part by the Royal Society grant Algorithmic and Combinatorial Aspects of Radio Communication, IJP - 2006/R2.
The research of E. Kantor and D. Peleg supported in part by grants from the Minerva Foundation and the Israel Ministry of Science.
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Gąsieniec, L., Kantor, E., Kowalski, D.R. et al. Time efficient k-shot broadcasting in known topology radio networks. Distrib. Comput. 21, 117–127 (2008). https://doi.org/10.1007/s00446-008-0058-0
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DOI: https://doi.org/10.1007/s00446-008-0058-0