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Bounds on the parallel evaluation of arithmetic expressions using associativity and commutativity

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Summary

We show that any arithmetic expression with n operands and parentheses nested to depth d can be evaluated in at most 1+2d+ [log2 n] steps, assuming that only associativity and commutativity are used to transform the expression. We also show that at most [n−2d/2] processors are needed to achieve this bound.

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Authors and Affiliations

  1. Department of Computer Science, University of Illinois at Urbana-Champaign, 61801, Urbana, Illinois, USA

    David Kuck

  2. Electrical Communication Laboratory Nippon Telephone and Telegraph Corporation, Tokyo, Japan

    Yoichi Muraoka

Authors
  1. David Kuck
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  2. Yoichi Muraoka
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Additional information

This work was supported in part by NSF Grant GJ 36936. An earlier version of this paper was presented at the Seventh Annual Princeton Conference on Information Sciences and Systems, March 1973.

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Kuck, D., Muraoka, Y. Bounds on the parallel evaluation of arithmetic expressions using associativity and commutativity. Acta Informatica 3, 203–216 (1974). https://doi.org/10.1007/BF00288634

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  • DOI: https://doi.org/10.1007/BF00288634

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