A simplicial algorithm for testing the integral properties of polytopes: A revision

Given an arbitrary polytope P in the n-dimensional Euclidean space R n , the question is to determine whether P contains an integral point or not. We propose a simplicial algorithm to answer this question based on a specifc integer labeling rule and a specific triangulation of R n . Starting from an arbitrary integral point ofR n , the algorithm terminates within a finite number of steps with either an integral point in P or proving there is no integral point inP. One prominent feature of the algorithm is that the structure of the algorithm is very simple and itcanbeeasily implemented on a computer. Moreover, the algorithm is computationally very simple, exible and stable.