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Analysis of a class of k-dimensional merge procedures, with an application to 2D Delaunay Triangulation in expected linear time after two-directional sorting (Extended Abstract)

By Christophe Lemaire and Jean-Michel Moreau


This paper exploits the notion of "unfinished sites" in the average-case analysis of k-dimensional divide-and-conquer algorithms. This general result is then applied to the 2D case, and it is shown that the divide-and-conquer construction of the Delaunay triangulation of a set of planar points quasi-uniformly distributed in a square may be done in expected linear time after a two-directional preprocessing sort. This method is readily implemented, and, as shown by the easily reproduced results provided, it is one of the fastest worst-case optimal methods ever suggested to construct real-scale Delaunay triangulations in the plane

Year: 1993
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