Mathematische Annalen

, Volume 287, Issue 1, pp 163–174 | Cite as

Simultaneously good bases of a lattice and its reciprocal lattice

  • Johan Håstad
  • Jeffrey C. Lagarias


Good Basis Reciprocal Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Babai, L.: On Lovàsz' lattice reduction and the nearest lattice point problem. combinatorica6, 1–13 (1986)Google Scholar
  2. 2.
    Cassels, J.W.S.: An introduction to the geometry of numbers. Berlin Heidelberg New York: Springer 1971Google Scholar
  3. 3.
    Cassels, J.W.S.: Rational quadratic forms. New York: Academic Press 1978Google Scholar
  4. 4.
    Hastad, J.: Dual vectors and lower bounds for the nearest lattice point problem. Combinatorica8, 75–81 (1988)Google Scholar
  5. 5.
    Hastad, J., Just, B., Lagarias, J.C., Schnorr, C.P.: Polynomial time algorithms for finding integer relations among real numbers. SIAM J. Comput.18, 859–881 (1989). Preliminary version in: Proc. STACS' 86, (Lect. Notes Comput. Sci. vol. 210, pp. 105–118). Berlin Heidelberg New York: Springer 1986Google Scholar
  6. 6.
    Kanman, R.: Minkowski's convex body theorem and integer programming. Math. Oper. Res.12, 415–440 (1987)Google Scholar
  7. 7.
    Lagarias, J.C., Lenstra, H.W.Jr., Schnorr, C.P.: Korkin-Zolotarev bases and successive minima of a lattice and its reciprocal lattice. Combinatorica, to appearGoogle Scholar
  8. 8.
    Lekkerkerker, C.: Geometry of numbers. Amsterdam: North-Holland 1969Google Scholar
  9. 9.
    Lenstra, A.K., Lenstra, H.W. Jr., Lovàsz, L.: Factoring polynomials with rational coefficients. Math. Ann.261, 513–534 (1982)Google Scholar
  10. 10.
    Mahler, K.: A theorem on inhomogeneous diophantine inequalities. Proc. Kon. Ned. Acad. Wet.41, 634–637 (1938)Google Scholar
  11. 11.
    Schnorr, C.P.: A hierarchy of polynomial time lattice basis reduction algorithms. Theor. Comp. Sci.53, 201–227 (1987)Google Scholar
  12. 12.
    Schnorr, C.P.: A more efficient algorithm for lattice basis reduction. J. Algorithms9, 47–62 (1988)Google Scholar
  13. 13.
    Schönhage, A.: Factorization of univariate integer polynomials by diphantine approximation and an improved basis reduction algorithm. Proc. 11th ICALP. Antwerpen 1984 (Lect. Notes Comp. Sci. vol. 182, pp. 13–20) Berlin Heidelberg New York: Springer 1985Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Johan Håstad
    • 1
  • Jeffrey C. Lagarias
    • 2
  1. 1.Royal Institute of TechnologyStockholmSweden
  2. 2.AT&T Bell LaboratoriesMurray HillUSA

Personalised recommendations