Abstract
An easily implemented modification to the divide-and-conquer algorithm for computing the Delaunay triangulation ofn sites in the plane is presented. The change reduces its Θ(n logn) expected running time toO(n log logn) for a large class of distributions that includes the uniform distribution in the unit square. Experimental evidence presented demonstrates that the modified algorithm performs very well forn≤216, the range of the experiments. It is conjectured that the average number of edges it creates—a good measure of its efficiency—is no more than twice optimal forn less than seven trillion. The improvement is shown to extend to the computation of the Delaunay triangulation in theL p metric for 1<p≤∞.
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Communicated by Bernard Chazelle.
This research was supported by National Science Foundation Grants DCR-8352081 and DCR-8416190.
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Dwyer, R.A. A faster divide-and-conquer algorithm for constructing delaunay triangulations. Algorithmica 2, 137–151 (1987). https://doi.org/10.1007/BF01840356
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DOI: https://doi.org/10.1007/BF01840356