Skip to main content Accesibility Help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article
  • Cited by 12
  • Cited by
    Crossref Citations
    Crossref logo
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    BAI, ZAI-QIAO and FINCH, STEVEN R. 2018. PRECISE CALCULATION OF HAUSDORFF DIMENSION OF APOLLONIAN GASKET. Fractals, Vol. 26, Issue. 04, p. 1850050.
    Forrester, Peter J. and Zhang, Jiyuan 2018. Volumes and distributions for random unimodular complex and quaternion lattices. Journal of Number Theory, Vol. 190, Issue. , p. 1.
    Iosifescu, Marius 2014. Spectral analysis for the Gauss problem on continued fractions. Indagationes Mathematicae, Vol. 25, Issue. 4, p. 825.
    2012. Zeta and q-Zeta Functions and Associated Series and Integrals. p. 603.
    Prellberg, Thomas 2003. Towards a complete determination of the spectrum of a transfer operator associated with intermittency. Journal of Physics A: Mathematical and General, Vol. 36, Issue. 10, p. 2455.
    Akhavi, Ali 2003. The optimal LLL algorithm is still polynomial in fixed dimension. Theoretical Computer Science, Vol. 297, Issue. 1-3, p. 3.
    Vallée, Brigitte 2003. Dynamical analysis of a class of Euclidean algorithms. Theoretical Computer Science, Vol. 297, Issue. 1-3, p. 447.
    Clément, J. Flajolet, P. and Vallée, B. 2001. Dynamical sources in information theory: A general analysis of trie structures. Algorithmica, Vol. 29, Issue. 1-2, p. 307.
    Vallée, B. 2001. Dynamical sources in information theory: Fundamental intervals and word prefixes. Algorithmica, Vol. 29, Issue. 1-2, p. 262.
    Bourdon, Jérémie Nebel, Markus and Vallée, Brigitte 2001. On the Stack-Size of General Tries. RAIRO - Theoretical Informatics and Applications, Vol. 35, Issue. 2, p. 163.
    Flajolet, Philippe and Salvy, Bruno 1998. Euler Sums and Contour Integral Representations. Experimental Mathematics, Vol. 7, Issue. 1, p. 15.
    Flajolet, Philippe and Vallée, Brigitte 1998. Continued fraction algorithms, functional operators, and structure constants. Theoretical Computer Science, Vol. 194, Issue. 1-2, p. 1.
    ×
  • Get access
    Add to cart USD35.00
    Check if you have access via personal or institutional login
    Log in Register

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

  • HERVÉ DAUDÉ (a1), PHILIPPE FLAJOLET (a2) and BRIGITTE VALLÉE (a3)
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, its probability distribution decays geometrically, and the dynamics are 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.

Copyright
1997 Cambridge University Press
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed

Cancel
Confirm
×