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- W2754588407 abstract "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 $P times Delta^m$, for a (small) natural number $m$ of our choice. $Delta^m$ 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." @default.
- W2754588407 created "2017-09-25" @default.
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- W2754588407 date "2002-01-01" @default.
- W2754588407 modified "2023-10-17" @default.
- W2754588407 title "Asymptotically efficient triangulations of the d -cube." @default.
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