Abstract
We introduce randomized K-dimensional binary search trees (randomized Kd-trees), a variant of K-dimensional binary search trees that allows the efficient maintenance of multidimensional records for any sequence of insertions and deletions; and thus, is fully dynamic. We show that several types of associative queries are efficiently supported by randomized Kd-trees. In particular, a randomized Kd-tree with n records answers exact match queries in expected O(log n) time. Partial match queries are answered in expected O(n1-f(s/K)) time, when s out of K attributes are specified (with 0 < f(s/K) < 1 a real valued function of s/K). Nearest neighbor queries are answered on-line in expected O(log n) time. Our randomized algorithms guarantee that their expected time bounds hold irrespective of the order and number of insertions and deletions.
This work is supported by the CONACyT grant # 89422 and by the ESPRIT-LTR Project ALCOM-IT contract # 20244.
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Duch, A., Estivill-Castro, V., Martínez, C. (1998). Randomized K-Dimensional Binary Search Trees. In: Chwa, KY., Ibarra, O.H. (eds) Algorithms and Computation. ISAAC 1998. Lecture Notes in Computer Science, vol 1533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49381-6_22
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DOI: https://doi.org/10.1007/3-540-49381-6_22
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