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Let F(x) be a convex function defined in R", which is symmetric about the origin an homogeneous of degree 1, and let L be the lattice of integers Zn. A ...
We show that the basis vector b1, in a reduced basis, is an approximation to a shortest nonzero lattice point with respect to F and relate the basis vectors bi ...
We show that the basis vector b1, in a reduced basis, is an approximation to a shortest non-zero lattice point with respect to F and relate the basis vectors bi ...
The results lead to an algorithm for integer programming which executes in polynomial time for fixed n, but which avoids the ellipsoidal approximations required ...
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What is the generalized reduced gradient GRG algorithm?
What is the reduction algorithm?
The general basis reduction algorithm requires the solution of many linear pro- grams, and there are tradeoffs between using an ellipsoidal approximation to ...
discussion of reduced bases we refer to the reader to the paper of Lovász and Scarf[15]. 3. Implementation. Carrying out the generalized basis reduction ...
We show that the basis vector b 1, in a reduced basis, is an approximation to a shortest nonzero lattice point with respect to F and relate the basis vectors b ...
The idea of basis reduction in two dimensional lattice is to find the orthogonal basis based on the given basis. The basis we found in Gauss algorithm is not ...
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The generalized Gauss algorithm, analyzed by Kaib and Schnorr in [10] , is a fast algorithm for finding a reduced basis in dimension 2. As explained in [8], ...
The Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, ...