On the Löwner-John Ellipsoids of the Metric Polytope

Raziel Gartsman, Nati Linial

The collection of all $n$-point metric spaces of diameter $\le 1$ constitutes a polytope ${\mathcal{M}}_n\subset {\mathbb{R}}^{\left(\genfrac{}{}{0ex}{}{n}{2}\right)}$, called the \emph{Metric Polytope}. In th…