A quick estimate for the volume of a polyhedron

12/12/2021

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by   Alexander Barvinok, et al.

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Let P be a bounded polyhedron defined as the intersection of the non-negative orthant R^n_+ and an affine subspace of codimension m in R^n. We show that a simple and computationally efficient formula approximates the volume of P within a factor of γ^m, where γ >0 is an absolute constant. The formula provides the best known estimate for the volume of transportation polytopes from a wide family.