Optimal Sparsifiers for Minkowski Sums and Sums of Seminorms
We extend the recent work of Reis and Rothvoss on sparsifying sums of $\ell_1$ norms to the more general task of sparsifying (Minkowski) sums of centrally symmetric, convex sets. As our main result, we prove that for any $\varepsilon>0$ and centrally symmetric, convex sets $C_1, \ldots, C_m\subseteq\mathbb{R}^n$ there...