A polynomial time algorithm to approximate the mixed volume within a simply exponential factor

Leonid Gurvits

Let $\mathbf{K}=(K_1,...,K_n)$ be an $n$-tuple of convex compact subsets in the Euclidean space ${\mathbb{R}}^n$, and let $V(\cdot )$ be the Euclidean volume in ${\mathbb{R}}^n$. The Minkowski polynom…