Approximation Depth of Convex Polytopes

Egor Bakaev; Florestan Brunck; Amir Yehudayoff

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arXiv · 2507.07779

Approximation Depth of Convex Polytopes

Egor Bakaev·Florestan Brunck·Amir Yehudayoff

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Abstract

We study approximations of polytopes in the standard model for computing polytopes using Minkowski sums and (convex hulls of) unions. Specifically, we study the ability to approximate a target polytope by polytopes of a given depth. Our main results imply that simplices can only be ``trivially approximated''. On the way, we obtain a characterization of simplices as the only ``outer additive'' convex bodies.

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Egor Bakaev, Florestan Brunck, Amir Yehudayoff. 2025-07-10. Approximation Depth of Convex Polytopes. https://arxiv.org/abs/2507.07779

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