A revised simplex method with integer Q-matrices

Abstract

We describe a modification of the simplex formulas in which Q-matrices are used to implement exact computations with an integer multiprecision library. Our motivation comes from the need for efficient and exact incremental solvers in the implementation of constraint solving languages such as Prolog. We explain how to reformulate the problem and the different steps of the simplex algorithm. We compare some measurements obtained with integer and rational computations.