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Fast Integer Programming in Fixed Dimension

  • Friedrich Eisenbrand
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2832)

Abstract

It is shown that the optimum of an integer program in fixed dimension, which is defined by a fixed number of constraints, can be computed with O(s) basic arithmetic operations, where s is the binary encoding length of the input. This improves on the quadratic running time of previous algorithms which are based on Lenstra’s algorithm and binary search.

It follows that an integer program in fixed dimension, which is defined by m constraints, each of binary encoding length at most s, can be solved with an expected number of O(m + log(m)s) arithmetic operations using Clarkson’s random sampling algorithm.

Keywords

Integer Program Rational Number Arithmetic Operation Integer Point Integral Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Friedrich Eisenbrand
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

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