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Gossiping in vertex-disjoint paths mode in d-dimensional grids and planar graphs

Extended abstract
  • Juraj Hromkovič
  • Ralf Klasing
  • Elena A. Stöhr
  • Hubert Wagener
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 726)

Abstract

The communication modes (one-way and two-way mode) used for sending messages to processors of interconnection networks via vertex-disjoint paths in one communication step are investigated. The complexity of communication algorithms is measured by the number of communication steps (rounds). Here, the complexity of gossiping in grids and in planar graphs is investigated. The main results are the following:
  1. 1.

    Effective one-way and two-way gossip algorithms for d-dimensional grids, d≥2, are designed.

     
  2. 2.

    The lower bound 2 log2n −log2k −log2 log2n −2 is established on the number of rounds of every two-way gossip algorithm working on any graph of n nodes and vertex bisection k. This proves that the designed two-way gossip algorithms on d-dimensional grids, d≥3, are almost optimal, and it also shows that the 2-dimensional grid belongs to the best gossip graphs among all planar graphs.

     
  3. 3.

    Another lower bound proof is developed to get some tight lower bounds on one-way “well-structured” gossip algorithms on planar graphs (note that all gossip algorithms designed until now in vertexdisjoint paths mode are “well-structured”).

     

Keywords

Planar Graph Complete Graph Interconnection Network Communication Mode Outerplanar Graph 
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 1993

Authors and Affiliations

  • Juraj Hromkovič
    • 1
  • Ralf Klasing
    • 1
  • Elena A. Stöhr
    • 1
  • Hubert Wagener
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of PaderbornPaderbornGermany

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