Rapid almost-complete broadcasting in faulty networks

  • Authors:
  • Rastislav Královi;Richard Královi

  • Affiliations:
  • Department of Computer Science, Comenius University, Bratislava, Slovakia;Department of Computer Science, Comenius University, Bratislava, Slovakia and Department of Computer Science, ETH Zurich, Switzerland

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2009

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Abstract

This paper studies the problem of broadcasting in synchronous point-to-point networks, where one initiator owns a piece of information that has to be transmitted to all other vertices as fast as possible. The model of fractional dynamic faults with threshold is considered: in every step either a fixed number c(G)-1, where c(G) is the edge connectivity of the communication graph, or a fraction @a of sent messages can be lost depending on which quantity is larger. As the main result we show that in complete graphs and hypercubes it is possible to inform all but a constant number of vertices, exhibiting only a logarithmic slowdown, i.e. in time O(Dlogn) where D is the diameter of the network and n is the number of vertices. Moreover, for complete graphs under some additional conditions (sense of direction, or @a