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

CP Schnorr, M Euchner - Mathematical programming, 1994 - Springer
We report on improved practical algorithms for lattice basis reduction. We propose a
practical floating point version of the L 3-algorithm of Lenstra, Lenstra, Lovász (1982). We
present a variant of the L 3-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 at most a few hours on a UNISYS 6000/70 or …

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

CP Schnorr, M Euchner - International Symposium on Fundamentals of …, 1991 - Springer
We report on improved practical algorithms for lattice basis reduction. We present a variant
of the L 3-algorithm with “deep insertions” and a practical algorithm for blockwise Korkine-
Zolotarev reduction, a concept extending L 3-reduction, that has been introduced by Schnorr
(1987). Empirical tests show that the strongest of these algorithms solves almost all subset
sum problems with up to 58 random weights of arbitrary bit length within at most a few hours
on a UNISYS 6000/70 or within a couple of minutes on a SPARC 2 computer.
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