Abstract
We consider centralized deterministic broadcasting in radio networks. The aim is to design a polynomial algorithm, which, given a graph G, produces a fast broadcasting scheme in the radio network represented by G. The problem of finding an optimal broadcasting scheme for a given graph is NP-hard, hence we can only hope for a good approximation algorithm. We give a deterministic polynomial algorithm which produces a broadcasting scheme working in time \({\cal O}(D \log n + \log ^2 n)\), for every n-node graph of diameter D. It has been proved recently [15,16] that a better order of magnitude of broadcasting time is impossible unless \(NP \subseteq BPTIME(n^{{\cal O}(\log \log n)})\). In terms of approximation ratio, we have a \({\cal O}(\log (n/D))\)-approximation algorithm for the radio broadcast problem, whenever D=Ω (log n).
The work of the first author was supported in part by the KBN Grant 4T11C04425. Research of the second author supported in part by NSERC grant OGP 0008136 and by the Research Chair in Distributed Computing of the Université du Québec en Outaouais. Part of this work was done during the second author’s visit at the Max-Planck-Institut für Informatik.
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Kowalski, D.R., Pelc, A. (2004). Centralized Deterministic Broadcasting in Undirected Multi-hop Radio Networks. In: Jansen, K., Khanna, S., Rolim, J.D.P., Ron, D. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. RANDOM APPROX 2004 2004. Lecture Notes in Computer Science, vol 3122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27821-4_16
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DOI: https://doi.org/10.1007/978-3-540-27821-4_16
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