A performance analysis of network topologies in finding the roots of a polynomial

  • Michel Cosnard
  • Pierre Fraigniaud
Algorithmic Studies For Hypercube-Type Systems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 457)


This paper introduces the parallelization on a distributed memory multicomputer of two iterative methods for finding all the roots of a given polynomial. The parallel algorithms share the computation of the roots among the processors and perform a total exchange of the data at each step. Since the amount of communications is the main drawback of this approach, we study the effect of the network topology on the performance of the algorithms. Particularly, we show that among the different classical processors networks topologies (ring, 2d-torus or n-cube), the hypercube topology minimizes the communications. For each topology is computed the optimal number of processors. Experiments on the hypercube FPS T40 illustrate the results.

Key words

Parallel algorithms local memory parallel computers polynomial zeros simultaneous polynomial root-finders broadcasting 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Michel Cosnard
    • 1
  • Pierre Fraigniaud
    • 1
  1. 1.Laboratoire de l'Informatique du Parallélisme - IMAG ENS LyonLyon Cedex 07France

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