Abstract

We present an improvement over a former technique, Jump & Walk ([7]), to locate points in the Delaunay triangulation of n sites uniformly distributed in a square. The method uses a dynamically balanced search tree. It is also studied when applied to a static balanced 2-d tree. This paper gives expected time analyses when the query points are bounded away from the boundary of the triangulation: the proof for the unrestricted case is much more complex, and will be presented in another paper (in preparation). Keywords: Delaunay triangulation, height- and weight-balanced trees, 2-d trees, worst- and averagecase analysis, point location. 1 Introduction Let Sn = fs 1 ; s 2 ; : : : ; s n g be a set of n distinct points in the euclidean plane E 2 , called sites, and G a planar graph of size n, with vertex set Sn . The (planar) point location problem consists in identifying the face (edge or site in degenerate situations) of G containing a given query point q. This problem, first addressed...

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