Deterministic Broadcasting Time in Radio Networks of Unknown Topology

  • Authors:
  • Dariusz R. Kowalski;Andrzej Pelc

  • Affiliations:
  • -;-

  • Venue:
  • FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
  • Year:
  • 2002

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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 + log2n) 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.