Kissing polytopes
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915124606926848 |
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| author | Deza, Antoine Onn, Shmuel Pokutta, Sebastian Pournin, Lionel |
| author_facet | Deza, Antoine Onn, Shmuel Pokutta, Sebastian Pournin, Lionel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_18597 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Kissing polytopes Deza, Antoine Onn, Shmuel Pokutta, Sebastian Pournin, Lionel Metric Geometry Combinatorics Optimization and Control 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. |
| title | Kissing polytopes |
| topic | Metric Geometry Combinatorics Optimization and Control |
| url | https://arxiv.org/abs/2305.18597 |