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Communication complexity of PRAMs

  • Alok Aggarwal
  • Ashok K. Chandra
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 317)

Abstract

We propose a model for the concurrent read exclusive write PRAM that captures its communication and computational requirements. For this model, we present several results, including the following:

Two n×n matrices can be multiplied in O(n3/p) computation time and O(n2/p2/3) communication delay using p processors (for pn3 / log3/2n). Furthermore, these bounds are optimal for arithmetic on semirings (using +, × only). For sorting and for FFT graphs, it is shown that communication delay of Ω(n log n/(p log(n/p)) is required for pn/ log n. This bound is tight for FFT graphs; it is also shown to be tight for sorting provided pn1−ε for any fixed ε>0.

Given a binary tree, τ, with n leaves and height h, let D opt (τ) denote the minimum communication delay needed to compute τ. It is shown that Ω(log n)≤D opt (τ)≤\(O(\sqrt n )\), and \(\Omega (\sqrt h )\)D opt O(h), all bounds being the best possible. We also present a simple polynomial algorithm that generates a schedule for computing τ with at most 2D opt (τ) delay.

It is shown that the a communication delay-computation time tradeoff given by Papadimitriou and Ullman for a diamond dag can be achieved for essentially two values of the computation time. We also present DAGs that exhibit proper tradeoffs for a substantial range of time.

Keywords

Computation Time Binary Tree Directed Acyclic Graph Communication Complexity Global Memory 
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 1988

Authors and Affiliations

  • Alok Aggarwal
    • 1
  • Ashok K. Chandra
    • 1
  1. 1.IBM Research DivisionThomas J. Watson Research CenterYorktown Heights

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