Title: On the expected number of common edges in delaunay and greedy triangulation
Authors: Cho, Han-Gue
Citation: Journal of WSCG. 1997, vol. 5, no. 1-3, p. 50-59.
Issue Date: 1997
Publisher: Václav Skala - UNION Agency
Document type: článek
URI: http://wscg.zcu.cz/wscg1997/wscg97.htm
ISSN: 1213-6972 (print)
1213-6980 (CD-ROM)
1213-6964 (online)
Keywords: výpočetní geometrie;triangulace
Keywords in different language: computational geometry;triangulation
Abstract in different language: So far some average-case properties in the Delaunay and greedy triangulation were given by complicated probabilistic analysis. In this paper, we present a rather simpler proof on that the expected number of common edges between Delaunay and Greedy triangulation is at least 40% when points are uniformly distributed, where n is the number points in a convex planar region. Our analysis shows that the value c of o (c.n) expected number of common edges between two triangulations is greater than 1.26. That constant c = 1.26 implies that at least 40% of Delaunay edges are common to the edges of Greedy triangulation. Applying this property, we can easily find at least 1.26n greedy edges in linear time from a Delaunay triangulation, if points are uniformly distributed in a region. Finally we give two experimental results showing that in practice c approaches up to 2.7, which means about 90% edges are common between two triangulations.
Rights: © Václav Skala - UNION Agency
Appears in Collections:Volume 5, number 1-3 (1997)

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