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.

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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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