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Lattice basis reduction: Improved practical algorithms and solving subset sum problems. (English) Zbl 0829.90099
A practical floating point \(L^3\)-algorithm, \(L^3FP\), is presented that shows good stability according to empirical tests up to dimension 125 with integer entries of bit length up to 300. Moreover, a practical algorithm for block Korkin-Zolotarev reduction is proposed, and a variant of the Lenstra-Lenstra-Lovasz \(L^3\)-algorithm is introduced that uses “deep insertions”. For all the algorithms presented computational performance in solving subset sum problems is reported.
Reviewer: R.Euler (Brest)

MSC:
90C10 Integer programming
90C27 Combinatorial optimization
11Y16 Number-theoretic algorithms; complexity
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