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The Generalized Basis Reduction Algorithm


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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)

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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 946.

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Length: 22 pages
Date of creation: Jun 1990
Date of revision:
Publication status: Published in Mathematics of Operations Research (August 1992), 17(3): 751-764
Handle: RePEc:cwl:cwldpp:946

Note: CFP 818.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Reduced basis; lattice point; integer programming;


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Cited by:
  1. Sanjay Mehrotra & Zhifeng Li, 2011. "Branching on hyperplane methods for mixed integer linear and convex programming using adjoint lattices," Journal of Global Optimization, Springer, vol. 49(4), pages 623-649, April.
  2. William Cook & Thomas Rutherford & Herbert E. Scarf & David F. Shallcross, 1991. "An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming," Cowles Foundation Discussion Papers 990, Cowles Foundation for Research in Economics, Yale University.
  3. Aardal,Karen, 1997. "A decade of combinatorial optimization," Research Memorandum 044, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).


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