The Generalized Basis Reduction Algorithm

Herbert Scarf and Laszlo Lovasz
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Laszlo Lovasz: Eotvos Lorand University, Budapest

No 946, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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: Reduced basis; lattice point; integer programming (search for similar items in EconPapers)
Pages: 22 pages
Date: 1990-06
Note: CFP 818.
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Citations: View citations in EconPapers (2)

Published in Mathematics of Operations Research (August 1992), 17(3): 751-764

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