Efficient Information Exchange in the Random Phone-Call Model

  • Petra Berenbrink
  • Jurek Czyzowicz
  • Robert Elsässer
  • Leszek Gąsieniec
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6199)

Abstract

We consider the gossiping problem in the classical random phone-call model introduced by Demers et. al. ([6]). We are given a complete graph, in which every node has an initial message to be disseminated to all other nodes. In each step every node is allowed to establish a communication channel with a randomly chosen neighbour. Karp et al. [15] proved that it is possible to design a randomized procedure performing O(nloglogn) transmissions that accomplishes broadcasting in time O(logn), with probability 1 − n − 1.

In this paper we provide a lower bound argument that proves Ω(nlogn) message complexity for any O(logn)-time randomized gossiping algorithm, with probability 1 − o(1). This should be seen as a separation result between broadcasting and gossiping in the random phone-call model.

We study gossiping at the two opposite points of the time and message complexity trade-off. We show that one can perform gossiping based on exchange of O(n·logn/loglogn) messages in time O(log2 n/loglogn), and based on exchange of O(nloglogn) messages with the time complexity \(O(\sqrt n).\) Both results hold wit probability 1 − n − 1.

Finally, we consider a model in which each node is allowed to store a small set of neighbours participating in its earlier transmissions. We show that in this model randomized gossiping based on exchange of O(nloglogn) messages can be obtained in time O(logn), with probability 1 − n − 1.

Keywords

Random Walk Active Node Message Transmission Leader Election Message Complexity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Petra Berenbrink
    • 1
  • Jurek Czyzowicz
    • 2
  • Robert Elsässer
    • 3
  • Leszek Gąsieniec
    • 4
  1. 1.School of Computing ScienceSimon Fraser University 
  2. 2.Department of Computer ScienceUniversity of Quebec in Hull 
  3. 3.Institute for Computer ScienceUniversity of Freiburg 
  4. 4.Department of Computer ScienceUniversity of Liverpool 

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