2013 IEEE 54th Annual Symposium on Foundations of Computer Science (2002)

Vancouver, BC, Canada

Nov. 16, 2002 to Nov. 19, 2002

ISSN: 0272-5428

ISBN: 0-7695-1822-2

pp: 63

Andrzej Pelc , Université du Québec á Hull

Dariusz R. Kowalski , Uniwersytet Warszawski

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

null

CITATION

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

*2013 IEEE 54th Annual Symposium on Foundations of Computer Science*, vol. 00, no. , pp. 63, 2002, doi:10.1109/SFCS.2002.1181883