Expected time analysis for Delaunay point location

Abstract. 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 Θ( √ n) for the Green-Sibson rectilinear search, Θ(n) for Jump and Walk, Θ(n) for BinSearch and Walk (which uses a 1-dimensional search tree), Θ(n) for search based on a random 2-d tree, and Θ(logn) for search aided by a 2-d median tree.