Tight Bounds for Approximate Carathéodory and Beyond

Abstract

We give a deterministic nearly-linear time algorithm for approximating any point inside a convex polytope with a sparse convex combination of the polytope’s vertices. Our result provides a constructive proof for the Approximate Carathéodory Problem [2], which states that any point inside a polytope contained in the lp ball of radius D can be approximated to… (More)

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