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Reports (Research Report) Year : 1996

An Average-case Analysis of the Gaussian Algorithm for Lattice Reduction

Hervé Daudé
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Philippe Flajolet
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Brigitte Vallée

Abstract

The Gaussian algorithm for lattice reduction in dimension 2 is analysed under its standard version. It is found that, when applied to random inputs in a continuous model, the complexity is constant on average, 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. Analysis in the discrete model and detailed numerical data are also presented.

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Other [cs.OH]
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Dates and versions

inria-00073892 , version 1 (24-05-2006)

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  • HAL Id : inria-00073892 , version 1

Cite

Hervé Daudé, Philippe Flajolet, Brigitte Vallée. An Average-case Analysis of the Gaussian Algorithm for Lattice Reduction. [Research Report] RR-2798, INRIA. 1996. ⟨inria-00073892⟩
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