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Feasibility and complexity of broadcasting with random transmission failures
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Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
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ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
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Fast radio broadcasting with advice
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Improved lower bound for deterministic broadcasting in radio networks
Theoretical Computer Science
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Brief announcement: faster gossiping in bidirectional radio networks with large labels
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Oblivious k-shot broadcasting in ad hoc radio networks
CATS '11 Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119
Oblivious k-shot broadcasting in ad hoc radio networks
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
Information dissemination in unknown radio networks with large labels
Theoretical Computer Science
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We consider broadcasting in radio networks, modeled as undirected graphs, whose nodes know only their own label and labels of their neighbors. In every step every node acts either as a transmitter or as a receiver. A node acting as a transmitter sends a message which can potentially reach all of its neighbors. A node acting as a receiver in a given step gets a message if and only if exactly one of its neighbors transmits in this step.Bar-Yehuda, Goldreich, and Itai [J. Comput. System Sci., 45 (1992), pp. 104--126] considered broadcasting in this model. They claimed a linear lower bound on the time of deterministic broadcasting in such radio networks of diameter 3. This claim turns out to be incorrect in this model (although it is valid in a more pessimistic model [R. Bar-Yehuda, O. Goldreich, and A. Itai, Errata Regarding "On the time complexity of broadcast in radio networks: An exponential gap between determinism and randomization," http://www.wisdom.weizmann.ac.il/mathusers/oded/p\_bgi.html, 2002]). We construct an algorithm that broadcasts in logarithmic time on all graphs from the Bar-Yehuda, Goldreich, and Itai paper (BGI). Moreover, we show how to broadcast in sublinear time on all n-node graphs of diameter $o(\log \log n)$. On the other hand, we construct a class of graphs of diameter 4, such that every broadcasting algorithm requires time $\Omega(\sqrt[4]{n})$ on these graphs. In view of the randomized algorithm from BGI, running in expected time ${\cal O}(D \log n + \log ^2 n)$ on all $n$-node graphs of diameter D (cf. also a recent ${\cal O}(D \log (n/D) + \log ^2 n)$-time algorithm from [D. Kowalski and A. Pelc, Proceedings of the 22nd Annual ACM Symposium on Principles of Distributed Computing, Boston, 2003, pp. 73--82; A. Czumaj and W. Rytter, Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, Cambridge, MA, 2003, pp. 492--501]), our lower bound gives the first correct proof of an exponential gap between determinism and randomization in the time of radio broadcasting, under the considered model of radio communication.