Gridvoronoi: An Efficient Spatial Index for Nearest Neighbor Query Processing

Abstract

In this paper, based upon Voronoi Diagram, we propose GridVoronoi which is a novel spatial index that enables users to find the spatial nearest neighbour (NN) from two-dimensional (2D) datasets in almost O(1) time. GridVoronoi augments the Voronoi Diagram with a virtual grid to promptly find out (in a geometric space) which Voronoi cell contains the query point. It consists of an off-line data pre-processing phase and an on-line query processing phase. In the off-line phase, the digital geographical space is partitioned with a Voronoi Diagram and a virtual grid, respectively. Next, for each square unit (i.e., grid cell), the corresponding Voronoi cells that contain or intersect with this square are derived and kept in a hashmap-like structure. In the on-line phase, for each real-time spatial NN query, the algorithm first identifies which virtual square(s) contain(s) this query; then looks up the hashmap structure to find the corresponding Voronoi cell(s) for this grid cell and the final result for the query. Overall, GridVoronoi significantly reduces the time complexity in finding spatial NN in 2D space, thus improves the efficiency of real-time spatial NN queries and Location Based Services.