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arXiv · 2112.06322

A quick estimate for the volume of a polyhedron

Alexander Barvinok·Mark Rudelson
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Abstract

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

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Alexander Barvinok, Mark Rudelson. 2021-12-12. A quick estimate for the volume of a polyhedron. https://arxiv.org/abs/2112.06322

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