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International Conference on Parallel Architectures and Languages Europe

PARLE 1993: PARLE '93 Parallel Architectures and Languages Europe pp 104–119Cite as

Optimal mappings of m dimensional FFT communication to k dimensional mesh for arbitrary m and k

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 694))

Abstract

The FFT communication patterns are important to not only FFT algorithms, but also many other algorithms over one or higher dimensional. The mapping of m dimensional FFT communication to k dimensional mesh has previously been considered only for the following special cases (a) m=1 or 2, k=1 or 2, (b) m=1 or 2, k=log(n) where n is the size of the machine. In this paper, we present the optimal mappings of m dimensional FFT communication onto k dimensional mesh for arbitrary m and k. The mappings are optimal since the communication distances in the logarithmic steps sum to exactly the diameter of the mesh regardless of the dimension cr the shape of the mesh. An m-k shuffle permutation, which subsumes perfect shuffle, is introduced and used to derive some of the optimal mappings. As a by-product, an optimal broadcast algorithm over any dimensional mesh, including binary hypercube as a special case, is presented.

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Authors and Affiliations

  1. Department of Computer Science and Center for Complex Systems, Brandeis University, 02254, Waltham, MA, USA

    Z. George Mou & Xiaojing Wang

Authors
  1. Z. George Mou
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  2. Xiaojing Wang
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Arndt Bode Mike Reeve Gottfried Wolf

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© 1993 Springer-Verlag Berlin Heidelberg

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Mou, Z.G., Wang, X. (1993). Optimal mappings of m dimensional FFT communication to k dimensional mesh for arbitrary m and k. In: Bode, A., Reeve, M., Wolf, G. (eds) PARLE '93 Parallel Architectures and Languages Europe. PARLE 1993. Lecture Notes in Computer Science, vol 694. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56891-3_9

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  • DOI: https://doi.org/10.1007/3-540-56891-3_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56891-9

  • Online ISBN: 978-3-540-47779-2

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