Lattice basis reduction: Improved practical algorithms and solving subset sum problems

@article{Schnorr1994LatticeBR,
  title={Lattice basis reduction: Improved practical algorithms and solving subset sum problems},
  author={C. Schnorr and M. Euchner},
  journal={Mathematical Programming},
  year={1994},
  volume={66},
  pages={181-199}
}
We report on improved practical algorithms for lattice basis reduction. We propose a practical floating point version of theL3-algorithm of Lenstra, Lenstra, Lovász (1982). We present a variant of theL3-algorithm with “deep insertions” and a practical algorithm for block Korkin—Zolotarev reduction, a concept introduced by Schnorr (1987). Empirical tests show that the strongest of these algorithms solves almost all subset sum problems with up to 66 random weights of arbitrary bit length within… Expand
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References

SHOWING 1-10 OF 66 REFERENCES
A More Efficient Algorithm for Lattice Basis Reduction
  • C. Schnorr
  • Mathematics, Computer Science
  • J. Algorithms
  • 1988
  • 131
A Hierarchy of Polynomial Time Lattice Basis Reduction Algorithms
  • C. Schnorr
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 1987
  • 619
An Improved Low-Denisty Subset Sum Algorithm
  • 98
  • PDF
Solving low density subset sum problems
  • J. Lagarias, A. Odlyzko
  • Computer Science, Mathematics
  • 24th Annual Symposium on Foundations of Computer Science (sfcs 1983)
  • 1983
  • 439
  • PDF
The Generalized Basis Reduction Algorithm
  • 101
  • PDF
Algorithmic theory of numbers, graphs and convexity
  • L. Lovász
  • Mathematics, Computer Science
  • CBMS-NSF regional conference series in applied mathematics
  • 1986
  • 365
  • PDF
Simultaneous reduction of a lattice basis and its reciprocal basis
  • M. Seysen
  • Mathematics, Computer Science
  • Comb.
  • 1993
  • 123
...
1
2
3
4
5
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