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Binary Addition Chain on EREW PRAM

  • Conference paper
Algorithms and Architectures for Parallel Processing (ICA3PP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7017))

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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.

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Author information

Authors and Affiliations

  1. Department of Basic Science, Faculty of Engineering, Sinai University, Egypt

    Khaled A. Fathy

  2. Computer Science Division, Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt

    Hazem M. Bahig & Hatem M. Bahig

  3. Department of Mathematics, Faculty of Science, AlAzhar University, Egypt

    A. A. Ragb

Authors
  1. Khaled A. Fathy
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  2. Hazem M. Bahig
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  3. Hatem M. Bahig
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  4. A. A. Ragb
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Editor information

Editors and Affiliations

  1. School of Information Technology, Deakin University, Melbourne Burwood Campus, 221 Burwood Highway, 3125, Burwood, VIC, Australia

    Yang Xiang  & Wanlei Zhou  & 

  2. ICAR-CNR and University of Calabria, Via P. Bucci 41 C, 87036, Rende, CS, Italy

    Alfredo Cuzzocrea

  3. School of Information Technology, Deakin University, Geelong Waurn Ponds Campus, Pigdons Road, 3217, Geelong, VIC, Australia

    Michael Hobbs

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© 2011 Springer-Verlag Berlin Heidelberg

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Fathy, K.A., Bahig, H.M., Bahig, H.M., Ragb, A.A. (2011). Binary Addition Chain on EREW PRAM. In: Xiang, Y., Cuzzocrea, A., Hobbs, M., Zhou, W. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2011. Lecture Notes in Computer Science, vol 7017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24669-2_31

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  • DOI: https://doi.org/10.1007/978-3-642-24669-2_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24668-5

  • Online ISBN: 978-3-642-24669-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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