The Generalized Basis Reduction Algorithm

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Abstract

Let F(x) be a convex function defined in R^{n}), which is symmetric about the origin and homogeneous of degree 1, and let L be the lattice of integers Z^{n}. A definition of a reduced basis, b^{1},...,b^{n}, of the lattice with respect to the distance function F is presented, and we describe an algorithm which yields a reduced basis in polynomial time, for fixed n. In the special case in which the bodies {x : F(x)

Keywords

REDUCTION ALGORITHM
DISTANCE FUNCTION
GENERALIZED BASIS
CONVEX FUNCTION
BASIS REDUCTION
REDUCED BASIS
HOMOGENEOUS
INTEGERS Z
LATTICE

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