快速估算多面体的体积

Pub Date : 2024-04-24 DOI:10.1007/s11856-024-2615-z

Alexander Barvinok, Mark Rudelson

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引用次数: 0

摘要

假设 P 是一个有界多面体，定义为非负正交ℝn+ 与ℝn 中标度为 m 的仿射子空间的交集。我们证明，一个简单且计算效率高的公式可以将 P 的体积逼近到 γm 的系数之内，其中 γ > 0 是一个绝对常量。该公式是目前已知的对运输多边形体积的最佳估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A quick estimate for the volume of a polyhedron

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 ℝⁿ. 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.

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