منابع مشابه
Lll Reduction and a Conjecture of Gunnells
Paul Gunnells has developed an algorithm for computing actions of Hecke operators on arithmetic cohomology below the cohomological dimension. One version of his algorithm uses a conjecture concerning LLL-reduced matrices. We prove this conjecture for dimensions 2 through 5 and disprove it for all higher dimensions.
متن کاملAccelerated Slide- and LLL-Reduction
Given an LLL-basis B of dimension n = hk we accelerate slide-reduction with blocksize k to run under a reasonable assumption in 1 6 nh log1+ε α local SVP-computations in dimension k, where α ≥ 4 3 measures the quality of the given LLL-basis and ε is the quality of slide-reduction. If the given basis B is already slide-reduced for blocksize k/2 then the number of local SVP-computations for slide...
متن کاملPartial LLL Reduction
The Lenstra-Lenstra-Lovasz (LLL) reduction has wide applications in digital communications. It can greatly improve the speed of the sphere decoding (SD) algorithms for solving an integer least squares (ILS) problem and the performance of the Babai integer point, a suboptimal solution to the ILS problem. Recently Ling and Howgrave-Graham proposed the so-called effective LLL (ELLL) reduction. It ...
متن کاملFast LLL-type lattice reduction
We modify the concept of LLL-reduction of lattice bases in the sense of Lenstra, Lenstra, Lovász [LLL82] towards a faster reduction algorithm. We organize LLL-reduction in segments of the basis. Our SLLL-bases approximate the successive minima of the lattice in nearly the same way as LLL-bases. For integer lattices of dimension n given by a basis of length 2, SLLL-reduction runs in O(n) bit ope...
متن کاملLLL-reduction for integer knapsacks
Given a matrix A ∈ Zm×n satisfying certain regularity assumptions, a wellknown integer programming problem asks to find an integer point in the associated knapsack polytope P(A,b)= {x ∈R≥0 :Ax = b} or determine that no such point exists. We obtain an LLL-based polynomial time algorithm that solves the problem subject to a constraint on the location of the vector b.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2009
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-09-10131-4