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Binary Addition Chain on EREW PRAM

  • Khaled A. Fathy
  • Hazem M. Bahig
  • Hatem M. Bahig
  • A. A. Ragb
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7017)

Abstract

An addition chain for a natural number x of n bits is a sequence of numbers a 0, a 1, ... , a l , such that a 0 = 1, a l  = x, and a k  = a i  + a j with 0 ≤ i,j < k ≤ l. The addition chain problem is what is the minimal number of additions needed to compute x starting from 1? In this paper, we present a new parallel algorithm to generate a short addition chain for x. The algorithm has running time O(log2 n) using polynomial number processors under EREW PRAM (exclusive read exclusive write parallel random access machine). The algorithm is faster than previous algorithms and is based on binary method.

Keywords

Addition chain binary method parallel algorithm EREW PRAM 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Khaled A. Fathy
    • 1
  • Hazem M. Bahig
    • 2
  • Hatem M. Bahig
    • 2
  • A. A. Ragb
    • 3
  1. 1.Department of Basic Science, Faculty of EngineeringSinai UniversityEgypt
  2. 2.Computer Science Division, Department of Mathematics, Faculty of ScienceAin Shams UniversityCairoEgypt
  3. 3.Department of Mathematics, Faculty of ScienceAlAzhar UniversityEgypt

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