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Near-Optimal Oracle Bounds for Isotropic Rounding
We give optimal bounds, up to polylogarithmic factors, for rounding convex bodies to near-isotropic position. A convex body $B(0,r)\subseteq K\subseteq B(0,R)$ in $\R^n$ can be rounded using $\Ot(n^3)$ membership queries; the upper bound extends to logconcave distributions. We prove a matching $\Ome
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