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The LLL Algorithm is but one Lattice basis reduction algorithm. In fact the LLL Algorithm is sub-optimal. Other Lattice basis reduction algorithms include the KZ algorithm. I would think this page should be a list of known Lattice basis reduction algorithms rather than redirecting to a particular one.
This page does not cite MathWorld, even though the Applications section is clearly lifted verbatim from there. —Preceding unsigned comment added by 67.241.45.203 (talk) 15:37, 30 January 2009 (UTC)
References edit
Hi 70.23.69.70, Could you explain your objections to Chee-Keng Yap? You describe it as irrelevant (it has two chapters on lattice reduction) and as lecture notes (it's a textbook). Perhaps you have only looked at the online preprint? - the paper version is of better quality. Alternatively, perhaps you could suggest better books on lattice reduction. --catslash (talk) 09:03, 17 June 2010 (UTC)
"Factoring polynomials with rational coefficients" is a classic and much-cited paper, and is a good reference for lattice reduction (though obsolete as far as factoring polynomials is concerned). However, I'm still curious as to your objections to Yap. I originally added this reference because it was the source for my (albeit meagre) contributions to this page. As it is the only text I have to hand which says much about the subject, it would be the source for any future contributions I might make - and so it would be inconvenient if I wasn't allowed to cite it. By the way, it is cited 53 times --catslash (talk) 23:56, 18 June 2010 (UTC)
Algorithms edit
The "Algorithms" list could be much longer. One possible addition is a sieving algorithm, for which one reference is "A sieve algorithm for the shortest lattice vector problem" by Miklós Ajtai, Ravi Kumar, D. Sivakumar, Proceedings of the thirty-third annual ACM symposium on Theory of computingJuly 2001. Another important algorithm is "Hermite-Korkine-Zolotarev" reduction, for which one reference is P. Q. Nguyen and B. Vall´ee, Eds., The LLL Algorithm: Survey and Applications. Berlin, Germany: Springer-Verlag, 2009. Sanpitch (talk) 06:06, 14 December 2021 (UTC)
See also https://eprint.iacr.org/2023/237 — Preceding unsigned comment added by 5.57.21.50 (talk) 15:18, 30 October 2023 (UTC)