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Mathematical Methods of Operations Research

, Volume 53, Issue 3, pp 353–361 | Cite as

The integral basis method for integer programming

  • Utz-Uwe Haus
  • Matthias Köppe
  • Robert Weismantel

Abstract.

This paper introduces an exact algorithm for solving integer programs, neither using cutting planes nor enumeration techniques. It is a primal augmentation algorithm that relies on iteratively substituting one column by columns that correspond to irreducible solutions of certain linear diophantine inequalities. We demonstrate the algorithm's potential by testing it on some instances of the MIPLIB with up to 6000 variables.

Key words: integer programming Hilbert bases primal methods 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

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.de)DE

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