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Is Your Permutation Algorithm Unbiased for n ≠ 2m?

  • Michael Waechter
  • Kay Hamacher
  • Franziska Hoffgaard
  • Sven Widmer
  • Michael Goesele
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7203)

Abstract

Many papers on parallel random permutation algorithms assume the input size n to be a power of two and imply that these algorithms can be easily generalized to arbitrary n. We show that this simplifying assumption is not necessarily correct since it may result in a bias. Many of these algorithms are, however, consistent, i.e., iterating them ultimately converges against an unbiased permutation. We prove this convergence along with proving exponential convergence speed. Furthermore, we present an analysis of iterating applied to a butterfly permutation network, which works in-place and is well-suited for implementation on many-core systems such as GPUs. We also show a method that improves the convergence speed even further and yields a practical implementation of the permutation network on current GPUs.

Keywords

parallel random permutation butterfly network bias consistency GPU 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Michael Waechter
    • 1
  • Kay Hamacher
    • 2
  • Franziska Hoffgaard
    • 2
  • Sven Widmer
    • 1
  • Michael Goesele
    • 1
  1. 1.GRIS, TU DarmstadtGermany
  2. 2.Bioinformatics and Theoretical BiologyTU DarmstadtGermany

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