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arXiv 1302.3200cs.DMcs.CGmath.CO
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剥离网格

Peeling the Grid

Sariel Har-Peled, Bernard Lidický

摘要:

考虑由整数$n \times n$网格形成的点集,以及在每次迭代中从点集中移除其凸包的顶点的过程。在这里,我们证明了这个过程的迭代次数是O(n^{4/3});也就是说,$n\times n$网格的凸层数是Θ(n^{4/3})。

英文摘要:

Consider the set of points formed by the integer $n \times n$ grid, and the process that in each iteration removes from the point set the vertices of its convex-hull. Here, we prove that the number of iterations of this process is O(n^{4/3}); that is, the number of convex layers of the $n\times n$ grid is Θ(n^{4/3}).

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