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) (1997)  (Make Corrections)  
Christophe Lemaire, Jean-Michel Moreau

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Abstract: This paper exploits the notion of "unfinished sites" in the average-case analysis of k-dimensional divideand -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... (Update)

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BibTeX entry:   (Update)

@misc{ lemaire-analysis,
  author = "Christophe Lemaire and Jean-Michel Moreau",
  title = "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)",
  url = "citeseer.nj.nec.com/95461.html" }
Citations (may not include all citations):
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219   Primitives for the Manipulation of General Subdivisions and .. (context) - Guibas, Stolfi - 1985
49   Two algorithms for constructing a Delaunay triangulation (context) - Lee, Schachter - 1980
34   Higher-Dimensional Voronoi Diagrams in Linear Expected Time (context) - Dwyer - 1991
21   A faster divide-and-conquer algorithm for constructing Delau.. (context) - Dwyer - 1987
12   The expected extremes in a Delaunay triangulation - Bern, Eppstein et al. - 1991
10   Delaunay triangulation and the convex hull of n points in ex.. (context) - Maus - 1984
5   Constructing Delaunay triangulations by merging buckets in q.. (context) - Katajainen, Koppinen - 1988
5   Improvements of the incremental method for the Voronoi diagr.. (context) - Ohya, Iti et al. - 1984
1   convexes et polytopes (context) - Berger - 1974

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