Asymptotically efficient triangulations of the d-cube
| dc.creator | Orden, David | |
| dc.creator | Santos, Francisco | |
| dc.date | 2002-04-11 | |
| dc.date | 2003-03-10 | |
| dc.date.accessioned | 2026-07-07T04:47:39Z | |
| dc.date.available | 2026-07-07T04:47:39Z | |
| dc.description | Let $P$ and $Q$ be polytopes, the first of "low" dimension and the second of "high" dimension. We show how to triangulate the product $P \times Q$ efficiently (i.e., with few simplices) starting with a given triangulation of $Q$. Our method has a computational part, where we need to compute an efficient triangulation of $P \times Δ^m$, for a (small) natural number $m$ of our choice. $Δ^m$ denotes the $m$-simplex. Our procedure can be applied to obtain (asymptotically) efficient triangulations of the cube $I^n$: We decompose $I^n = I^k \times I^{n-k}$, for a small $k$. Then we recursively assume we have obtained an efficient triangulation of the second factor and use our method to triangulate the product. The outcome is that using $k=3$ and $m=2$, we can triangulate $I^n$ with $O(0.816^{n} n!)$ simplices, instead of the $O(0.840^{n} n!)$ achievable before. | |
| dc.description | 19 pages, 6 figures. Only minor changes from previous versions, some suggested by anonymous referees. Paper accepted in "Discrete and Computational Geometry" | |
| dc.identifier | https://arxiv.org/abs/math/0204157 | |
| dc.identifier | http://arxiv.org/abs/math/0204157 | |
| dc.identifier | Discrete Comput. Geom., 30:4 (2003), 509-528. | |
| dc.identifier | doi:10.1007/s00454-003-2845-5 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63797 | |
| dc.subject | Combinatorics | |
| dc.title | Asymptotically efficient triangulations of the d-cube | |
| dc.type | text |