# A quick estimate for the volume of a polyhedron

arXiv: https://arxiv.org/abs/2112.06322 · HTML: https://mlsanity.com/paper/2112.06322/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2021.

## Built on by (most cited first, 1 of 1)

- [Faster Sampling from Log-Concave Densities over Polytopes via Efficient Linear Solvers](https://mlsanity.com/paper/2409.04320/) (2024)

## Abstract (arXiv)

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