Theory of linear and integer programming
Theory of linear and integer programming
Integer and combinatorial optimization
Integer and combinatorial optimization
The D1-triangulation of Rn for simplicial algorithms for computing solutions of nonlinear equations
Mathematics of Operations Research
A Simplicial Approach to the Determination of An Integer Point of a Simplex
Mathematics of Operations Research
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An arbitrary starting variable dimension algorithm is proposed to compute an integer point of an n-dimensional simplex. It is based on an integer labeling rule and a triangulation of R^n. The algorithm consists of two interchanging phases. The first phase of the algorithm is a variable dimension algorithm, which generates simplices of varying dimensions,and the second phase of the algorithmforms a full-dimensional pivoting procedure, which generatesn-dimensional simplices. The algorithm varies from one phase to the other. When the matrix defining the simplex is in the so-called canonical form, starting at an arbitrary integer point, the algorithm within a finite number of iterations either yields an integer point of the simplex orproves that no such point exists.