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arXiv · 2610.08248

Exposition of an approximation algorithm for mixed volumes of a constant number of convex bodies

Hariharan Narayanan
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Abstract

We study $\varepsilon$-relative approximation of mixed volumes of a fixed number $k$ of full-dimensional convex bodies in $\mathbb{R}^n$, given membership oracles and a known bound $B_n\subseteq K_i\subseteq R_0B_n$. We present a randomized algorithm that estimates any prescribed mixed volume within relative error $\varepsilon$ with probability at least $1-δ$, using polynomially many oracle calls and bit operations in $n$, $\log R_0$, $\varepsilon^{-1}$, and $\logδ^{-1}$ for fixed $k$.

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Hariharan Narayanan. 2026-10-06. Exposition of an approximation algorithm for mixed volumes of a constant number of convex bodies. https://arxiv.org/abs/2610.08248

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