The Integral Basis Method for Integer Programming

by Haus, Utz-Uwe; Köppe, Matthias; Weismantel, Robert


Preprint series: 00-16, Preprints

90C10 Integer programming


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 prove that our algorithm is finite and demonstrate its potential by testing it on some instances of the MIPLIB with several hundred variables.

Keywords: Integer programming, Hilbert bases, primal methods

Notes: All authors supported by grants FKZ 0037KD0099 and FKZ 2495A/0028G of the Kultusministerium of Sachsen-Anhalt. Last author supported by a Gerhard-Hess-Preis and grant WE 1462 of the Deutsche Forschungsgemeinschaft, and by the European DONET program TMR ERB FMRX-CT98-0202.

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Letzte Änderung: 01.03.2018 - Ansprechpartner: Webmaster