On the expected number of common edges in delaunay and greedy triangulation
Han-Gue Cho · Digital Library (University of West Bohemia) · 1997
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.