FRS: Fast Range Search by Pruning Unnecessary Distance Computations Based on K-D Tree

We present a fast range search algorithm, which greatly reduces unnecessary distance computations, based on a technique to prune redundant distance computations. Theoretical and experimental analysis have shown that the proposed algorithm significantly improves the original k-D tree based algorithm, which runs in O(log(n)) time either in low dimension or the searching range is small. In the case where the searching range is large enough or it doesn't intersect with the data space, the proposed algorithm runs in O(1) time. The tradeoffs is that it costs extra distance computations for finding the maximum or minimum distance from a point to a hyper rectangle.