Kissing polytopes
Metric Geometry
2025-01-29 v2 Combinatorics
Optimization and Control
Abstract
We investigate the following question: how close can two disjoint lattice polytopes contained in a fixed hypercube be? This question stems from various contexts where the minimal distance between such polytopes appears in complexity bounds of optimization algorithms. We provide nearly matching lower and upper bounds on this distance and discuss its exact computation. We also give similar bounds in the case of disjoint rational polytopes whose binary encoding length is prescribed.
Keywords
Cite
@article{arxiv.2305.18597,
title = {Kissing polytopes},
author = {Antoine Deza and Shmuel Onn and Sebastian Pokutta and Lionel Pournin},
journal= {arXiv preprint arXiv:2305.18597},
year = {2025}
}
Comments
28 pages, 3 figures