The PKD-tree for Orthogonal d-Dimensional Range Search

We present two new d-dimensional data structures, called the PKD-tree and the PKD+-tree, respectively. They are explored for indexing combined text and point data in low and high dimensional data spaces, and evaluated experimentally for orthogonal range search (for 2 ≤ d ≤ 128 and n up to 1,000,000) using synthetic data points and real data. The experimental results show that the PKD-tree and the PKD+-tree work well for any d, and they always outperform the Pyramid technique, and are greatly better than the k-d tree and the R∗-tree when d ≥ log2 n. For a PKD+-tree built from n uniform and random data points, an orthogonal range search with a query square W of side length ∆ visits O(d log n + n(1− (1− 2∆)d)) nodes for ∆ ≤ 0.5.