k-d Range Search with Binary Patricia Tries

Abstract

We use Patricia tries to represent textual and spatial data, and present a range search algorithm for reporting all k-d records from a set of size n intersecting a query rectangle. Data and queries include both textual and spatial data. Patricia tries are evaluated experimentally (for n up to 1,000,000) using uniform distributed random spatial data and textual data selected from the Canadian toponymy. We compared the performance of the Patricia trie for k-d points, k-d rectangles and k-d combined textual and spatial data to the k-d tree, R*-tree, Ternary Search Trie and the naive method. Overall, our experiments show that Patricia tries are the best when F Є [0, log2 n] (F is the number of data in range). The expected range search time for Patricia tries was determined theoretically, and found to agree with experimental results when 2 <= k <= 20.