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.
Highlights
Due to the massive spread of smartphones and the development of precise positioning techniques, location-based services have become increasingly popular in everyday life
Spatial (K ) Nearest Neighbor (NN) search techniques can be used in many different real-life applications, including Location-Based Services (LBS), urban space planning [1], route planning [2], [3], positioning based on Internet of Things (IOT) [4]–[6], location verification/privacy protection [7]–[10], spatial data mining [11]–[15], etc
We investigate how to improve the efficiency of spatial NN query processing, which is a fundamental issue for top-k spatial keyword queries [16] and preference queries [17], location-aware recommendation [18], etc
Summary
Due to the massive spread of smartphones and the development of precise positioning techniques, location-based services have become increasingly popular in everyday life. We propose a method which is able to find an NN query’s nearest spatial object in 2D datasets in almost O(1) time We refer to this method as GridVoronoi since it uses a Voronoi Diagram [20], [21] blended with a virtual square grid for quickly accessing the corresponding location of the query in the geographical area and finding the nearest spatial object in almost O(1) time. In the online query processing phase, for each spatial NN query, GridVoronoi first calculates which square unit of the virtual grid contains this query It finds in the above hashmap the Voronoi cell that contain(s)/intersect(s) this square unit and returns the corresponding spatial data point for this Voronoi cell, as the query result.
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