An Approximate Nearest Neighbor Query Algorithm Based on Hilbert Curve

Querying k nearest neighbors of query point from data set in high dimensional space is one of important operations in spatial database. The classic nearest neighbor query algorithms are based on R-tree. However, R-tree exits overlapping problem of minimum bounding rectangles. This causes its time complexity exponentially depends on the dimensionality of the space. So, the reduction of the dimensionality is the key point. Hilbert curve fills high dimensional space linearly, divides the space into equal-size grids and maps points lying in grids into linear space. Using the quality of reducing dimensionality of Hilbert curve, the paper presents an approximate k nearest neighbor query algorithm AKNN, and analyzes the quality of k nearest neighbors in theory. According to the experimental result, the execution time of algorithm AKNN is shorter than the nearest neighbor query algorithm based on R-tree in high dimensional space, and the quality of approximate k nearest neighbors satisfies the need of real applications.