In computer science, a range tree is an ordered tree data structure to hold a list of points. It allows all points within a given range to be reported efficiently, and is typically used in two or higher dimensions. Range trees were introduced by Jon Louis Bentley in 1979.[1] Similar data structures were discovered independently by Lueker,[2] Lee and Wong,[3] and Willard.[4]
The range tree is an alternative to the k-d tree. Compared to k-d trees, range trees offer faster query times of (in Big O notation) but worse storage of , where n is the number of points stored in the tree, d is the dimension of each point and k is the number of points reported by a given query.
Bernard Chazelle improved this to query time and space complexity .[5][6]
^Bentley, J. L. (1979). "Decomposable searching problems" (PDF). Information Processing Letters. 8 (5): 244–251. doi:10.1016/0020-0190(79)90117-0. Archived from the original on September 24, 2017.
^Lueker, G. S. (1978). "A data structure for orthogonal range queries". 19th Annual Symposium on Foundations of Computer Science (sfcs 1978). pp. 28–21. doi:10.1109/SFCS.1978.1. S2CID 14970942.
^Lee, D. T.; Wong, C. K. (1980). "Quintary trees: A file structure for multidimensional database systems". ACM Transactions on Database Systems. 5 (3): 339. doi:10.1145/320613.320618. S2CID 2547376.
^Willard, Dan E. The super-b-tree algorithm (Technical report). Cambridge, MA: Aiken Computer Lab, Harvard University. TR-03-79.
^Chazelle, Bernard (1990). "Lower Bounds for Orthogonal Range Searching: I. The Reporting Case" (PDF). Journal of the ACM. 37 (2): 200–212. doi:10.1145/77600.77614. S2CID 8895683.
^Chazelle, Bernard (1990). "Lower Bounds for Orthogonal Range Searching: II. The Arithmetic Model" (PDF). Journal of the ACM. 37: 439–463. doi:10.1145/79147.79149. S2CID 15935619.
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