On the positive sum property and the computation of Graver test sets

In the first part of this paper we discuss the positive sum property, a property inherent to LP, IP, and MIP Graver test sets, and develop, based on that property, a common notational and algorithmic framework for Graver test sets. Moreover, we show how to find an initial feasible solution with the help of universal test sets and deal with termination of the augmentation algorithm that improves this solution to optimality.