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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)

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  • Herbert E. Scarf & Laszlo Lovasz, 1990. "The Generalized Basis Reduction Algorithm," Cowles Foundation Discussion Papers 946, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:946
    Note: CFP 818.
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    Cited by:

    1. William Cook & Thomas Rutherford & Herbert E. Scarf & David Shallcross, 1993. "An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 5(2), pages 206-212, May.
    2. Herbert Scarf, 1994. "The Allocation of Resources in the Presence of Indivisibilities," Journal of Economic Perspectives, American Economic Association, vol. 8(4), pages 111-128, Fall.
    3. 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.

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