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Partitioning space for range queries
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Yao, F. Frances, Dobkin, David P., Edelsbrunner, Herbert and Paterson, Michael S. (1988) Partitioning space for range queries. University of Warwick. Department of Computer Science. (Department of Computer Science research report). (Unpublished)
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Abstract
It is shown that, given a set S of n points in R3, one can always find three planes that form an eight-partition of S, that is, a partition where at most n/8 points of S lie in each of the eight open regions. This theorem is used to define a data structure, called an octant tree, for representing any point set in R3. An octant tree for n points occupies O(n) space and can be constructed in polynomial time. With this data structure and its refinements, efficient solutions to various range query problems in 2 and 3 dimensions can be obtained, including (1) half-space queries: find all points of S that lie to one side of any given plane; (2) polyhedron queries: find all points that lie inside (outside) any given polyhedron; and (3) circular queries in R2: for a planar set S, find all points that lie inside (outside) any given circle. The retrieval time for all these queries is T(n)=O(na + m) where a= 0.8988 (or 0.8471 in case (3)) and m is the size of the output. This performance is the best currently known for linear-space data structures which can be deterministically constructed in polynomial time.
| Item Type: | Report | ||||
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| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science > Computer Science | ||||
| Library of Congress Subject Headings (LCSH): | Partitions (Mathematics), Trees (Graph theory) | ||||
| Series Name: | Department of Computer Science research report | ||||
| Publisher: | University of Warwick. Department of Computer Science | ||||
| Official Date: | March 1988 | ||||
| Dates: |
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| Number: | Number 118 | ||||
| Number of Pages: | 18 | ||||
| DOI: | CS-RR-118 | ||||
| Institution: | University of Warwick | ||||
| Theses Department: | Department of Computer Science | ||||
| Status: | Not Peer Reviewed | ||||
| Publication Status: | Unpublished | ||||
| Publisher Statement: | F.F. Yao, D. Dobkin, H. Edelsbrunner and M.S. Paterson, “Partitioning Space for Range Queries”, <i>SIAM Journal on Computation</i> <b>18</b>, pp. 371-384 (1989) | ||||
| Funder: | Xerox Corporation, Science and Engineering Research Council (Great Britain) (SERC) | ||||
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