Given a set of points in IR , called sites, we consider the problem of approximating the Voronoi cell of a site by a convex polyhedron with a small number of facets or, equivalently, of finding a small set of approximate Voronoi neighbors of . More precisely, we define an -approximate Voronoi neighborhood of , denoted , to be a subset of satisfying the following property: is an -approximate nea...

In this paper we consider fast nearest-neighbor search techniques based on the projections of Voronoi regions. The Voronoi diagram of a given set of points provides an implicit geometric interpretation of nearest-neighbor search and serves as an important basis for several proximity search algorithms in computational geometry and in developing structure-based fast vector quantization techniques...

Using the domain-theoretic model for geometric computation, we define the partial Delaunay triangulation and the partial Voronoi diagram of N partial points in R2 and show that these operations are domain-theoretically computable and effectively computable with respect to Hausdorff distance and Lebesgue measure. These results are obtained by showing that the map which sends three partial points...

The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define many variants of Voronoi diagrams depending on the class of objects, the distance functions and the embedding space. In this paper, we investigate a framework...

The Network Voronoi diagram and its variants have been extensively used in the context of numerous applications in road networks, particularly to efficiently evaluate various spatial proximity queries such as k nearest neighbor (kNN), reverse kNN, and closest pair. Although the existing approaches successfully utilize the network Voronoi diagram as a way to partition the space for their specifi...

This paper considers the eeect of site perturbations on Voronoi diagrams, where the sites are points in the plane. Given a bound on the distance that any site may move, we ask which pairs of Voronoi neighbors may become non-neighbors and which are guaranteed to remain neighbors. A pair of the second kind is called stable. The paper shows necessary and suucient conditions for stability. Algorith...

Whilst a geographical information system may use many different representations of areal data, the vector format is the most commonly utilized structure. Although some researchers consider it efficient, others comment on its drawbacks. The potential exists for the implementation of another format with improved attributes and capabilities. This paper presents a method of creating a hybrid Vorono...