Indexing network Voronoi diagrams

Abstract

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 specific problems, there is little emphasis on how to efficiently find and access the network Voronoi cell containing a particular point or edge of the network. In this paper, we study the index structures on network Voronoi diagrams that enable exact and fast response to contain query in road networks. We show that existing index structures, treating a network Voronoi cell as a simple polygon, may yield inaccurate results due to the network topology, and fail to scale to large networks with numerous Voronoi generators. With our method, termed Voronoi-Quad-tree (or VQ-tree for short), we use Quad-tree to index network Voronoi diagrams to address both of these shortcomings. We demonstrate the efficiency of VQ-tree via experimental evaluations with real-world datasets consisting of a variety of large road networks with numerous data objects. © 2012 Springer-Verlag.