Better Late than Never: the Complexity of Arrangements of Polyhedra
Fuente:
arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
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| _version_ | 1866908595006734336 |
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| author | Aronov, Boris Bae, Sang Won Cabello, Sergio Cheong, Otfried Eppstein, David Knauer, Christian Seidel, Raimund |
| author_facet | Aronov, Boris Bae, Sang Won Cabello, Sergio Cheong, Otfried Eppstein, David Knauer, Christian Seidel, Raimund |
| contents | Let $\mathcal{A}$ be the subdivision of $\mathbb{R}^d$ induced by $m$ convex polyhedra having $n$ facets in total. We prove that $\mathcal{A}$ has combinatorial complexity $O(m^{\lceil d/2 \rceil} n^{\lfloor d/2 \rfloor})$ and that this bound is tight. The bound is mentioned several times in the literature, but no proof for arbitrary dimension has been published before. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03960 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Better Late than Never: the Complexity of Arrangements of Polyhedra Aronov, Boris Bae, Sang Won Cabello, Sergio Cheong, Otfried Eppstein, David Knauer, Christian Seidel, Raimund Computational Geometry Metric Geometry Let $\mathcal{A}$ be the subdivision of $\mathbb{R}^d$ induced by $m$ convex polyhedra having $n$ facets in total. We prove that $\mathcal{A}$ has combinatorial complexity $O(m^{\lceil d/2 \rceil} n^{\lfloor d/2 \rfloor})$ and that this bound is tight. The bound is mentioned several times in the literature, but no proof for arbitrary dimension has been published before. |
| title | Better Late than Never: the Complexity of Arrangements of Polyhedra |
| topic | Computational Geometry Metric Geometry |
| url | https://arxiv.org/abs/2506.03960 |