Computing an Integer Point of a Class of Polytopes with an Arbitrary Starting Variable Dimension Algorithm

Abstract An arbitrary starting variable dimension algorithm is developed for computing an integer point of a polytope, P = {x | Ax ≤ b}, which satisfies that each row of A has at most one positive entry. The algorithm is derived from an integer labelling rule and a triangulation of the space. It consists of two phases, one of which forms a variable dimension algorithm and the other a full-dimensional pivoting procedure. Starting at an arbitrary integer point, the algorithm interchanges from one phase to the other, if necessary, and follows a finite simplicial path that either leads to an integer point of the polytope or proves that no such point exists.