Abstract Given an arbitrary polytope P in the п-dimensional Euclidean
space Rn, 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 specific integer labeling rule and a specific triangulation
of Rn. Starting from an arbitrary integral point of K'. the algorithm
terminates within a finite number of steps with either an integral point
in P or proving there is no integral point in P. One prominent feature
of the algorithm is that the structure of the algorithm is very simple and
it can be easily implemented on a computer. Moreover, the algorithm
is computationally very simple, flexible and stable.
Keywords: Polytope, integral point, simplicial method, integer linear
programming.
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