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Vancouver, BC, Canada

Nov. 16, 2002 to Nov. 19, 2002

ISBN: 0-7695-1822-2

pp: 63

Dariusz R. Kowalski , Uniwersytet Warszawski

Andrzej Pelc , Université du Québec á Hull

ABSTRACT

In a seminal paper [3], Bar-Yehuda, Goldreich and Itai considered broadcasting in radio networks whose nodes know only their own label and labels of their neighbors. They claimed a linear lower bound on the time of deterministic broadcasting in such radio networks, by constructing a class of graphs of diameter 3, with the property that every broadcasting algorithm requires linear time on one of these graphs. Due to a subtle error in the argument, this result is incorrect. We construct an algorithm that broadcasts in logarithmic time on all graphs from [3]. Moreover, we show how to broadcast in sublinear time on all n -node graphs of diameter 0(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 one of these graphs. In view of the randomized algorithm from [3], runnning in expected time O(Dlogn + log<sup>2</sup>n) on all n -node graphs of diameter D, our lower bound gives the first correct proof of an exponential gap between determinism and randomization in the time of radio broadcasting.

INDEX TERMS

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CITATION

Dariusz R. Kowalski,
Andrzej Pelc,
"Deterministic Broadcasting Time in Radio Networks of Unknown Topology",

*FOCS*, 2002, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science 2002, pp. 63, doi:10.1109/SFCS.2002.1181883