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

**Series:** 2000-16, Preprints

- MSC:
- 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