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Annual Symposium on Theoretical Aspects of Computer Science

STACS 1985: STACS 85 pp 173–179Cite as

An algorithm to construct Minkowski-reduced lattice-bases

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 182))

Abstract

This paper presents an algorithm M-RED, which constructs Minkowski-reduced bases for lattices of arbitrary dimension n. For n fixed, the running time is polynomial in the length of the input.

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References

  1. J.W.S.Cassels, "An Introduction to the Geometry of Numbers", Heidelberg 1959

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  2. B. Helfrich, "Reduktionsalgorithmen für Gitterbasen", Diplomarbeit, Frankfurt 1984

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  3. R.Kannan, "Improved Algorithms for Integer Programming and Related Lattice Problems", in 15th ACM Symposium on Theory of Computing, 1983

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  4. J.C.Lagarias, "Worst-Case Complexity Bounds for Algorithms in the Theory of Integral Quadratic Forms", in Journal of Algorithms, 1980

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  5. A.K.Lenstra, H.W.Lenstra, L.Lovàsz, "Factoring Polynomials with Rational Coefficients", Report 82-05, Mathematisch Instituut, Universiteit Amsterdam, 1982

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  6. B.L. van der Waerden, H.Gross, "Studien zur Theorie der Quadratischen Formen", Basel 1968.

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik der J.W.Goethe-Universität, Robert-Mayer-Str. 6-10, D-6000, Frankfurt/Main

    Bettina Helfrich

Authors
  1. Bettina Helfrich
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Editor information

K. Mehlhorn

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© 1984 Springer-Verlag Berlin Heidelberg

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Helfrich, B. (1984). An algorithm to construct Minkowski-reduced lattice-bases. In: Mehlhorn, K. (eds) STACS 85. STACS 1985. Lecture Notes in Computer Science, vol 182. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024006

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  • DOI: https://doi.org/10.1007/BFb0024006

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13912-6

  • Online ISBN: 978-3-540-39136-4

  • eBook Packages: Springer Book Archive

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