Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Information Processing Letters
New data structures for orthogonal range queries
SIAM Journal on Computing
The power of geometric duality
BIT - Ellis Horwood series in artificial intelligence
Adding range restriction capability to dynamic data structures
Journal of the ACM (JACM)
Computational geometry: an introduction
Computational geometry: an introduction
Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
Halfplanar range search in linear space and O(n0.695) query time
Information Processing Letters
New upper bounds for neighbor searching
Information and Control
Information and Control
Halfspace range search: an algorithmic application of k-sets
Discrete & Computational Geometry
Filtering search: a new approach to query answering
SIAM Journal on Computing
A general approach to d-dimensional geometric queries
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
On k-hulls and related problems
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Space searching for intersecting objects
Journal of Algorithms
Partitioning and geometric embedding of range spaces of finite Vapnik-Chervonenkis dimension
SCG '87 Proceedings of the third annual symposium on Computational geometry
Functional approach to data structures and its use in multidimensional searching
SIAM Journal on Computing
Efficient data structures for range searching on a grid
Journal of Algorithms
Partitioning space for range queries
SIAM Journal on Computing
A randomized algorithm for closest-point queries
SIAM Journal on Computing
Lines in space-combinators, algorithms and applications
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
An optimal-time algorithm for slope selection
SIAM Journal on Computing
Applications of random sampling in computational geometry, II
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Partition trees for triangle counting and other range searching problems
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Combinatorial complexity bounds for arrangements of curves and spheres
Discrete & Computational Geometry - Special issue on the complexity of arrangements
Lower bounds for orthogonal range searching: I. The reporting case
Journal of the ACM (JACM)
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
Lower bounds for orthogonal range searching: part II. The arithmetic model
Journal of the ACM (JACM)
Implicitly representing arrangements of lines or segments
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Quasi-optimal range searching in spaces of finite VC-dimension
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Partitioning arrangements of lines, part II: applications
Discrete & Computational Geometry
Discrete & Computational Geometry - Selected papers from the fifth annual ACM symposium on computational geometry, Saarbrücken, Germany, June 5-11, 1989
Solving query-retrieval problems by compacting Voronoi diagrams
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
A fast planar partition algorithm, II
Journal of the ACM (JACM)
Approximations and optimal geometric divide-and-conquer
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Randomized multidimensional search trees (extended abstract): dynamic sampling
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
A singly exponential stratification scheme for real semi-algebraic varieties and its applications
Theoretical Computer Science
Computational Geometry: Theory and Applications
Cutting hyperplane arrangements
Discrete & Computational Geometry
Small-dimensional linear programming and convex hulls made easy
Discrete & Computational Geometry
Randomized optimal algorithm for slope selection
Information Processing Letters
Randomized multidimensional search trees: lazy balancing and dynamic shuffling (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Dynamic maintenance of geometric structures made easy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Randomized multidimensional search trees: further results in dynamic sampling (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
A general approach to removing degeneracies
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Efficient point location in a convex spatial cell-complex
SIAM Journal on Computing
Applications of parametric searching in geometric optimization
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Using separation algorithms in fixed dimension
Journal of Algorithms
Good splitters for counting points in triangles
Journal of Algorithms
An efficient approach to removing geometric degeneracies
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Incidence and nearest-neighbor problems for lines in 3-space
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Ray shooting in convex polytopes
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Strongly polynomial-time and NC algorithms for detecting cycles in periodic graphs
Journal of the ACM (JACM)
Journal of Algorithms
Applications of a new space-partitioning technique
Discrete & Computational Geometry
Reporting points in halfspaces
Computational Geometry: Theory and Applications
On vertical ray shooting in arrangements
Computational Geometry: Theory and Applications
Approximating center points with iterated radon points
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Efficient exact arithmetic for computational geometry
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
An expander-based approach to geometric optimization
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Cutting hyperplanes for divide-and-conquer
Discrete & Computational Geometry
On the zone of a surface in a hyperplane arrangement
Discrete & Computational Geometry
Finding stabbing lines in 3-space
Discrete & Computational Geometry
Counting circular arc intersections
SIAM Journal on Computing
Ray shooting and parametric search
SIAM Journal on Computing
Almost tight upper bounds for the single cell and zone problems in three dimensions
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
An algorithm for approximate closest-point queries
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Point location among hyperplanes and unidirectional ray-shooting
Computational Geometry: Theory and Applications
On linear-time deterministic algorithms for optimization problems in fixed dimension
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
On degeneracy in geometric computations
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Mathematical Techniques for Efficient Record Segmentation in Large Shared Databases
Journal of the ACM (JACM)
Parametric Combinatorial Computing and a Problem of Program Module Distribution
Journal of the ACM (JACM)
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Multidimensional divide-and-conquer
Communications of the ACM
Design of Dynamic Data Structures
Design of Dynamic Data Structures
Partitioning Point Sets in 4 Dimensions
Proceedings of the 12th Colloquium on Automata, Languages and Programming
Lower Bounds on the Complexity of Simplex Range Reporting on a Pointer Machine
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
The Nature and Meaning of Perturbations in Geometric Computing
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
On Spanning Trees with Low Crossing Numbers
Data Structures and Efficient Algorithms, Final Report on the DFG Special Joint Initiative
Scaling and related techniques for geometry 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
Building Voronoi Diagrams for Convex Polygons in Linear Expected Time
Building Voronoi Diagrams for Convex Polygons in Linear Expected Time
On Stabbing Lines for Convex Polyhedra in 3D
On Stabbing Lines for Convex Polyhedra in 3D
Dynamic Half-Space Range Reporting and Its Application
Dynamic Half-Space Range Reporting and Its Application
SPHERE PACKING NUMBERS FOR SUBSETS OF THE BOOLEAN n-CUBE WITH BOUNDED VAPNIK-CHERVONENKIS DIMENSION
SPHERE PACKING NUMBERS FOR SUBSETS OF THE BOOLEAN n-CUBE WITH BOUNDED VAPNIK-CHERVONENKIS DIMENSION
Fixed-dimensional linear programming queries made easy
Proceedings of the twelfth annual symposium on Computational geometry
Paul Erdös (1913-996): his influence on the theory of computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Space-time tradeoffs for emptiness queries (extended abstract)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Efficient searching with linear constraints
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
On enumerating and selecting distances
Proceedings of the fourteenth annual symposium on Computational geometry
Efficient generation of k-directional assembly sequences
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Fast software for box intersections
Proceedings of the sixteenth annual symposium on Computational geometry
Lower bounds for intersection searching and fractional cascading in higher dimension
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Improving min/max aggregation over spatial objects
Proceedings of the 9th ACM international symposium on Advances in geographic information systems
The power of nonmonotonicity in geometric searching
Proceedings of the eighteenth annual symposium on Computational geometry
Efficient aggregation over objects with extent
Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Algorithmic issues in modeling motion
ACM Computing Surveys (CSUR)
Fast Range Searching with Delaunay Triangulations
Geoinformatica
Temporal and spatio-temporal aggregations over data streams using multiple time granularities
Information Systems - Special issue: Best papers from EDBT 2002
Temporal Aggregation over Data Streams Using Multiple Granularities
EDBT '02 Proceedings of the 8th International Conference on Extending Database Technology: Advances in Database Technology
2-D Spatial Indexing Scheme in Optimal Time
ADBIS-DASFAA '00 Proceedings of the East-European Conference on Advances in Databases and Information Systems Held Jointly with International Conference on Database Systems for Advanced Applications: Current Issues in Databases and Information Systems
Irregularities of Distribution, Derandomization, and Complexity Theory
FST TCS 2000 Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science
Approximate similarity retrieval with M-trees
The VLDB Journal — The International Journal on Very Large Data Bases
Sublinear geometric algorithms
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Lower bounds for intersection searching and fractional cascading in higher dimension
Journal of Computer and System Sciences - STOC 2001
Range counting over multidimensional data streams
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Optimizing spatial Min/Max aggregations
The VLDB Journal — The International Journal on Very Large Data Bases
On the importance of idempotence
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The effect of corners on the complexity of approximate range searching
Proceedings of the twenty-second annual symposium on Computational geometry
On the stabbing number of a random Delaunay triangulation
Computational Geometry: Theory and Applications
On regular vertices on the union of planar objects
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Efficient indexing methods for probabilistic threshold queries over uncertain data
VLDB '04 Proceedings of the Thirtieth international conference on Very large data bases - Volume 30
Relative Convex Hulls in Semi-dynamic Subdivisions
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Approximate range searching: The absolute model
Computational Geometry: Theory and Applications
Two-dimensional range search based on the Voronoi diagram
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
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
Algorithms and theory of computation handbook
3D block-based medial axis transform and chessboard distance transform based on dominance
Image and Vision Computing
Indexing for vector projections
DASFAA'11 Proceedings of the 16th international conference on Database systems for advanced applications: Part II
Querying simplexes in quasi-triangulation
Computer-Aided Design
Polyline fitting of planar points under min-sum criteria
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Regular and non-regular point sets: Properties and reconstruction
Computational Geometry: Theory and Applications
approximate range searching: the absolute model
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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In geometric range searching, algorithmic problems of the following type are considered. Given an n-point set P in the plane, build a data structure so that, given a query triangle R, the number of points of P lying in R can be determined quickly. Similar questions can be asked for point sets in higher dimensions, with triangles replaced by simplices or by more complicated shapes. Algorithms of this type are of crucial importance in computational geometry, as they can be used as subroutines in solutions to many seemingly unrelated problems, which are often motivated by practical applications, for instance in computer graphics (ray tracing, hidden-surface removal etc.). We present a survey of theoretical results and the main techniques in geometric range searching.