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An efficient parallel block-reduction algorithm

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Algorithmic Number Theory (ANTS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1423))

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Abstract

In this paper, we present a new parallel block-reduction algorithm for reducing lattice bases which allows the use of an arbitrarily chosen block-size between two and n where n denotes the dimension of the lattice. Thus, we are building a hierarchy of parallel lattice basis reduction algorithms between the known parallel all-swap algorithm which is a parallelization for block-size two and the reduction algorithm for block-size n which corresponds to the known sequential lattice basis reduction algorithm. We show that even though the parallel all-swap algorithm as well as the parallel block-reduction algorithm have the same asymptotic complexity in respect to arithmetic operations in theory, in practice neither block-size two nor block-size n are a priori the best choices. The optimal block-size in respect to minimizing the reduction time rather depends strongly on the used parallel system and the corresponding communication costs.

The research was done while the author was a member of the Graduiertenkolleg Informatik at the UniversitÄt des Saarlandes (Saarbrücken), a fellowship program of the DFG (Deutsche Forschungsgemeinschaft).

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Authors and Affiliations

  1. FTK/A, Daimler Benz AG, HPC 0507, D-70564, Stuttgart, Germany

    Susanne Wetzel

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  1. Susanne Wetzel
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Joe P. Buhler

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© 1998 Springer-Verlag Berlin Heidelberg

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Wetzel, S. (1998). An efficient parallel block-reduction algorithm. In: Buhler, J.P. (eds) Algorithmic Number Theory. ANTS 1998. Lecture Notes in Computer Science, vol 1423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054872

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  • DOI: https://doi.org/10.1007/BFb0054872

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64657-0

  • Online ISBN: 978-3-540-69113-6

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