Basis of solutions for a system of linear inequalities in integers: Computation and applications

Abstract

We define a basis of solutions of a system of linear inequalities and present a general algorithm for finding such a basis. Our algorithm relies on an algorithm for finding a Hilbert basis for the set of nonnegative solutions of a system of linear inequalities and can be used in conjunction with any such algorithm. © Springer-Verlag Berlin Heidelberg 2005.