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Mathematical Programming

, Volume 96, Issue 2, pp 205–246 | Cite as

A primal all-integer algorithm based on irreducible solutions

  • Utz-Uwe Haus
  • Matthias Köppe
  • Robert Weismantel

Abstract.

 This paper introduces an exact primal augmentation algorithm for solving general linear integer programs. The algorithm iteratively substitutes one column in a tableau by other columns that correspond to irreducible solutions of certain linear diophantine inequalities. We prove that various versions of our algorithm are finite. It is a major concern in this paper to show how the subproblem of replacing a column can be accomplished effectively. An implementation of the presented algorithms is given. Computational results for a number of hard 0/1 integer programs from the MIPLIB demonstrate the practical power of the method.

Keywords

Computational Result Integer Program Linear Integer Program Diophantine Inequality Augmentation Algorithm 
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

  • Utz-Uwe Haus
    • 1
  • Matthias Köppe
    • 1
  • Robert Weismantel
    • 1
  1. 1.Otto-von-Guericke-Universität Magdeburg, Department of Mathematics/IMO, Universitätsplatz 2, 39106 Magdeburg, Germany. e-mail: {haus, mkoeppe, weismant}@imo.math.uni-magdeburg.deDE

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