Fast searching in a real algebraic manifold with applications to geometric complexity
Proc. of the international joint conference on theory and practice of software development (TAPSOFT) Berlin, March 25-29, 1985 on Mathematical foundations of software development, Vol. 1: Colloquium on trees in algebra and programming (CAAP'85)
On k-hulls and related problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
A 3-space partition and its applications
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Epsilon-nets and simplex range queries
SCG '86 Proceedings of the second annual symposium on Computational geometry
Further applications of random sampling to computational geometry
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Partitioning and geometric embedding of range spaces of finite Vapnik-Chervonenkis dimension
SCG '87 Proceedings of the third annual symposium on Computational geometry
ACM SIGACT News
Lines in space-combinators, algorithms and applications
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Quasi-Valid range querying and its implications for nearest neighbor problems
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Cutting hyperplane arrangements
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
How to net a lot with little: small &egr;-nets for disks and halfspaces
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Quasi-optimal upper bounds for simplex range searching and new zone theorems
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
ACM SIGACT News
An algorithm for generalized point location and its applications
Journal of Symbolic Computation
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
How hard is halfspace range searching?
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
A deterministic algorithm for the three-dimensional diameter problem
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
ACM Computing Surveys (CSUR)
Efficient collision detection for moving polyhedra
Proceedings of the eleventh annual symposium on Computational geometry
Computing faces in segment and simplex arrangements
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Two algorithms for nearest-neighbor search in high dimensions
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Locality-preserving hashing in multidimensional spaces
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A cost model for nearest neighbor search in high-dimensional data space
PODS '97 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Efficient search for approximate nearest neighbor in high dimensional spaces
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Lower bounds for high dimensional nearest neighbor search and related problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Approximate nearest neighbor queries in fixed dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
On linear-time deterministic algorithms for optimization problems in fixed dimension
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
An optimal algorithm for approximate nearest neighbor searching
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Tighter bounds for nearest neighbor search and related problems in the cell probe model
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Deterministic algorithms for 3-D diameter and some 2-D lower envelopes
Proceedings of the sixteenth annual symposium on Computational geometry
Proceedings of the sixteenth annual symposium on Computational geometry
Maintaining approximate extent measures of moving points
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
ACM Computing Surveys (CSUR)
Active Storage for Large-Scale Data Mining and Multimedia
VLDB '98 Proceedings of the 24rd International Conference on Very Large Data Bases
Tighter lower bounds for nearest neighbor search and related problems in the cell probe model
Journal of Computer and System Sciences - Special issue on STOC 2000
Approximating extent measures of points
Journal of the ACM (JACM)
A strong lower bound for approximate nearest neighbor searching
Information Processing Letters
Mobile services discovery and selection in the publish/subscribe paradigm
CASCON '04 Proceedings of the 2004 conference of the Centre for Advanced Studies on Collaborative research
Diamond: A Storage Architecture for Early Discard in Interactive Search
FAST '04 Proceedings of the 3rd USENIX Conference on File and Storage Technologies
Crossing patterns of semi-algebraic sets
Journal of Combinatorial Theory Series A
Nearly equal distances and Szemerédi's regularity lemma
Computational Geometry: Theory and Applications - Special issue on the Japan conference on discrete and computational geometry 2004
On the diameter of separated point sets with many nearly equal distances
European Journal of Combinatorics - Special issue on extremal and probabilistic combinatorics
Polytope range searching and integral geometry
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Computational Geometry: Theory and Applications
Nearly equal distances and Szemerédi's regularity lemma
Computational Geometry: Theory and Applications - Special issue on the Japan conference on discrete and computational geometry 2004
Catching elephants with mice: Sparse sampling for monitoring sensor networks
ACM Transactions on Sensor Networks (TOSN)
Proceedings of the twenty-sixth annual symposium on Computational geometry
Diamond: a storage architecture for early discard in interactive search
FAST'04 Proceedings of the 3rd USENIX conference on File and storage technologies
Proceedings of the twenty-seventh annual symposium on Computational geometry
A comparison of nearest neighbor search algorithms for generic object recognition
ACIVS'06 Proceedings of the 8th international conference on Advanced Concepts For Intelligent Vision Systems
Optimal private halfspace counting via discrepancy
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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It is shown that any bounded region in Ed can be divided into 2d subregions of equal volume in such a way that no hyperplane in Ed can intersect all 2d of the subregions. This theorem provides the basis of a data structure scheme for organizing n points in d dimensions. Under this scheme, a broad class of geometric queries in d dimensions, including many common problems in range search and optimization, can be solved in linear storage space and sublinear time.