Space-time tradeoff for answering range queries (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
Epsilon-nets and simplex range queries
SCG '86 Proceedings of the second annual symposium on Computational geometry
Linear data structures for two types of range search
SCG '86 Proceedings of the second annual symposium on Computational geometry
A general approach to d-dimensional geometric queries
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Quasi-optimal upper bounds for simplex range searching and new zone theorems
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Solving query-retrieval problems by compacting Voronoi diagrams
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
How hard is halfspace range searching?
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Approximating center points with iterated radon points
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
A deterministic linear time algorithm for geometric separators and its applications
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
ACM Computing Surveys (CSUR)
On the partitionability of point sets in space (preliminary report)
SCG '85 Proceedings of the first annual symposium on Computational geometry
A computational geometry approach to clustering problems
SCG '85 Proceedings of the first annual symposium on Computational geometry
On k-hulls and related problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
An optimal generalization of the centerpoint theorem, and its extensions
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Polytope range searching and integral geometry
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
An optimal extension of the centerpoint theorem
Computational Geometry: Theory and Applications
Centerpoints and Tverberg's technique
Computational Geometry: Theory and Applications
Proceedings of the twenty-sixth annual symposium on Computational geometry
Tight lower bounds for halfspace range searching
Proceedings of the twenty-sixth annual symposium on Computational geometry
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Let S be a set of n points in three-dimensional space. It is shown that one can always find three planes that divide S into eight open regions, of which no seven together contain more than &agr; n points where &agr; is a constant octant-tree, for representing any point set in 3-space. Efficient solutions to various data retrieval problems are readily available with this structure. For example, using octant-trees, one can answer in sublinear time T (n) @@@@O(n0.98) 1) half-space queries: find all points of S that lie to one side of a plane P; 2) polytope queries: find all points that lie inside (outside) a polytope; and 3) circular queries in E2: given a planar set S, find all points that lie within (without) a circle of radius r and center c for any r and c. An octant-tree for n points occupies O(n) space and can be constructed with O(n4) preprocessing time.