Expected time analysis for Delaunay point location

We consider point location in Delaunay triangulations with the aid of simple data structures. In particular, we analyze methods in which a simple data structure is used to first locate a point close to the query point. For points uniformly distributed on the unit square, we show that the expected point location complexities are ( n) for the Green-Sibson rectilinear search, (n1/3 ) for Jump and Walk, (n1/4 ) for BinSearch and Walk (which uses a 1-dimensional search tree), (n0.056... ) for search based on a random 2-d tree, and (log n) for search aided by a 2-d median tree. Keywords and phrases. Delaunay triangulation, Voronoi diagram, point location, computational geometry, expected time analysis, random tree, probabilistic analysis. CR Categories: 3.74, 5.25, 5.5.

• Type: Journal
• Year: 2004
• Where: COMGEO
• Authors: Luc Devroye, Christophe Lemaire, Jean-Michel Moreau
• Keywords: Applied Computing, COMGEO 2004, Delaunay Triangulation, Point Location, Simple Data Structure