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Topology of parallel networks and computational complexity (extended abstract)

  • Juraj Hromkovič
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 657)

Abstract

It is shown that there are such (natural) computing problems that one needs a strongly connected network topology to compute them effectively. For instance, some one-output Boolean function f (corresponding to a deterministic context-free language) requiring exponential number of processors to be computed in polylogarithmic time by unbounded-degree networks with polylogarithmic separators (for instance, trees) is presented. If one restricts the computing model to bounded-degree networks with polylogarithmic separators then f cannot be computed in polylogarithmic time (independently on the number of processors used). The results of this kind are generalized in a trade-off among time, number of processors, separator of the network and the communication complexity of the problem computed. These results are extended also for a probabilistic model of parallel networks.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Juraj Hromkovič
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of PaderbornPaderbornGermany

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