Approximation Depth of Convex Polytopes
Metric Geometry
2025-07-11 v1 Computational Geometry
Machine Learning
Combinatorics
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.
Keywords
Cite
@article{arxiv.2507.07779,
title = {Approximation Depth of Convex Polytopes},
author = {Egor Bakaev and Florestan Brunck and Amir Yehudayoff},
journal= {arXiv preprint arXiv:2507.07779},
year = {2025}
}