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)


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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