An analysis of the Gaussian algorithm for lattice reduction

  • Hervé Daudé
  • Philippe Flajolet
  • Brigitte Vallée
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 877)


The Gaussian algorithm for lattice reduction in dimension 2 (under both the standard version and the centered version) is analysed. It is found that, when applied to random inputs, the complexity is asymptotically constant, the probability distribution decays geometrically, and the dynamics is characterized by a conditional invariant measure. The proofs make use of connections between lattice reduction, continued fractions, continuants, and functional operators. Detailed numerical data are also presented.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Hervé Daudé
    • 1
  • Philippe Flajolet
    • 2
  • Brigitte Vallée
    • 3
  1. 1.Département de MathématiquesUniversité de ProvenceMarseille Cedex 3France
  2. 2.INRIA-RocquencourtLe ChesnayFrance
  3. 3.Département d'InformatiqueUniversité de CaenCaenFrance

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