Object representation by means of nonminimal division quadtrees and octrees
ACM Transactions on Graphics (TOG)
Computational geometry: an introduction
Computational geometry: an introduction
A consistent hierarchical representation for vector data
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Optimal quadtree construction algorithms
Computer Vision, Graphics, and Image Processing
An object centered hierarchical representation for 3D objects: the prism tree
Computer Vision, Graphics, and Image Processing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Digitizing the plane with cells of nonuniform size
Information Processing Letters
The BANG file: A new kind of grid file
SIGMOD '87 Proceedings of the 1987 ACM SIGMOD international conference on Management of data
A population analysis for hierarchical data structures
SIGMOD '87 Proceedings of the 1987 ACM SIGMOD international conference on Management of data
Efficient Component Labeling of Images of Arbitrary Dimension Represented by Linear Bintrees
IEEE Transactions on Pattern Analysis and Machine Intelligence
Neighbor finding in images represented by octrees
Computer Vision, Graphics, and Image Processing
Applications of spatial data structures: Computer graphics, image processing, and GIS
Applications of spatial data structures: Computer graphics, image processing, and GIS
The design and analysis of spatial data structures
The design and analysis of spatial data structures
A New Region Expansion for Quadtrees
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
The LSD tree: spatial access to multidimensional and non-point objects
VLDB '89 Proceedings of the 15th international conference on Very large data bases
The fieldtree: a data structure for geographic information systems
SSD '90 Proceedings of the first symposium on Design and implementation of large spatial databases
The arc tree: an approximation scheme to represent arbitrary curved shapes
Computer Vision, Graphics, and Image Processing
The buddy tree: an efficient and robust access method for spatial data base
Proceedings of the sixteenth international conference on Very large databases
A survey of ray tracing acceleration techniques
An introduction to ray tracing
The R*-tree: an efficient and robust access method for points and rectangles
SIGMOD '90 Proceedings of the 1990 ACM SIGMOD international conference on Management of data
Tree visualization with tree-maps: 2-d space-filling approach
ACM Transactions on Graphics (TOG)
A qualitative comparison study of data structures for large line segment databases
SIGMOD '92 Proceedings of the 1992 ACM SIGMOD international conference on Management of data
Hashing by proximity to process duplicates in spatial databases
CIKM '94 Proceedings of the third international conference on Information and knowledge management
OBBTree: a hierarchical structure for rapid interference detection
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
The SR-tree: an index structure for high-dimensional nearest neighbor queries
SIGMOD '97 Proceedings of the 1997 ACM SIGMOD international conference on Management of data
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Storing a collection of polygons using quadtrees
ACM Transactions on Graphics (TOG)
The Java programming language (2nd ed.)
The Java programming language (2nd ed.)
Efficient processing of window queries in the pyramid data structure
PODS '90 Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
The Grid File: An Adaptable, Symmetric Multikey File Structure
ACM Transactions on Database Systems (TODS)
Distance browsing in spatial databases
ACM Transactions on Database Systems (TODS)
Connected Component Labeling Using Quadtrees
Journal of the ACM (JACM)
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
An Algorithm for Finding Best Matches in Logarithmic Expected Time
ACM Transactions on Mathematical Software (TOMS)
Computer Processing of Line-Drawing Images
ACM Computing Surveys (CSUR)
ACM Computing Surveys (CSUR)
Data Structures for Range Searching
ACM Computing Surveys (CSUR)
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
Communications of the ACM
A quadtree medial axis transform
Communications of the ACM
Strip trees: a hierarchical representation for curves
Communications of the ACM
Region representation: quadtrees from boundary codes
Communications of the ACM
Region representation: boundary codes from quadtrees
Communications of the ACM
Multidimensional binary search trees used for associative searching
Communications of the ACM
Communications of the ACM
PK-tree: a spatial index structure for high dimensional point data
Information organization and databases
The K-D-B-tree: a search structure for large multidimensional dynamic indexes
SIGMOD '81 Proceedings of the 1981 ACM SIGMOD international conference on Management of data
R-trees: a dynamic index structure for spatial searching
SIGMOD '84 Proceedings of the 1984 ACM SIGMOD international conference on Management of data
Communications of the ACM
Use of the SAND spatial browser for digital government applications
Communications of the ACM
Spatial Searching in Geometric Databases
Proceedings of the Fourth International Conference on Data Engineering
Similarity Indexing with the SS-tree
ICDE '96 Proceedings of the Twelfth International Conference on Data Engineering
The R+-Tree: A Dynamic Index for Multi-Dimensional Objects
VLDB '87 Proceedings of the 13th International Conference on Very Large Data Bases
Benchmarking Spatial Join Operations with Spatial Output
VLDB '95 Proceedings of the 21th International Conference on Very Large Data Bases
Filter Trees for Managing Spatial Data over a Range of Size Granularities
VLDB '96 Proceedings of the 22th International Conference on Very Large Data Bases
The clustering Property of Corner Transformation for Spatial Database Applications
COMPSAC '99 23rd International Computer Software and Applications Conference
Efficient Processing of Spatial Queries in Line Segment Databases
SSD '91 Proceedings of the Second International Symposium on Advances in Spatial Databases
SSD '95 Proceedings of the 4th International Symposium on Advances in Spatial Databases
Visualizing and Animating R-trees and Spatial Operations in Spatial Databases on the Worldwide Web
VDB4 Proceedings of the IFIP TC2/WG 2.6 Fourth Working Conference on Visual Database Systems 4
VDB4 Proceedings of the IFIP TC2/WG 2.6 Fourth Working Conference on Visual Database Systems 4
The ATREE: A Data Structure to Support Very Large Scientific Databases
ISD '99 Selected Papers from the International Workshop on Integrated Spatial Databases, Digital Inages and GIS
VASCO: visualizing and animating spatial constructs and operations
Proceedings of the nineteenth annual symposium on Computational geometry
On visible surface generation by a priori tree structures
SIGGRAPH '80 Proceedings of the 7th annual conference on Computer graphics and interactive techniques
Efficient octree conversion by connectivity labeling
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
The quad-CIF tree: A data structure for hierarchical on-line algorithms
DAC '82 Proceedings of the 19th Design Automation Conference
Data Redundancy and Duplicate Detection in Spatial Join Processing
ICDE '00 Proceedings of the 16th International Conference on Data Engineering
Efficient computation and data structures for graphics.
Efficient computation and data structures for graphics.
Efficient structures for geometric data management
Efficient structures for geometric data management
Tree-Maps: a space-filling approach to the visualization of hierarchical information structures
VIS '91 Proceedings of the 2nd conference on Visualization '91
Index-driven similarity search in metric spaces (Survey Article)
ACM Transactions on Database Systems (TODS)
Big Omicron and big Omega and big Theta
ACM SIGACT News
Decoupling partitioning and grouping: Overcoming shortcomings of spatial indexing with bucketing
ACM Transactions on Database Systems (TODS)
A Distributed Quadtree Index for Peer-to-Peer Settings
ICDE '05 Proceedings of the 21st International Conference on Data Engineering
Foundations of Multidimensional and Metric Data Structures (The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling)
Efficient query processing on spatial networks
Proceedings of the 13th annual ACM international workshop on Geographic information systems
ACM Transactions on Database Systems (TODS)
Using a distributed quadtree index in peer-to-peer networks
The VLDB Journal — The International Journal on Very Large Data Bases
Client-Based Spatial Browsing on the World Wide Web
IEEE Internet Computing
Scalable network distance browsing in spatial databases
Proceedings of the 2008 ACM SIGMOD international conference on Management of data
A dichromatic framework for balanced trees
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
A polyhedron representation for computer vision
AFIPS '75 Proceedings of the May 19-22, 1975, national computer conference and exposition
A Fast Similarity Join Algorithm Using Graphics Processing Units
ICDE '08 Proceedings of the 2008 IEEE 24th International Conference on Data Engineering
Distance Oracles for Spatial Networks
ICDE '09 Proceedings of the 2009 IEEE International Conference on Data Engineering
Path oracles for spatial networks
Proceedings of the VLDB Endowment
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An overview is presented of a number of representations of multidimensional data that arise in spatial applications. Multidimensional spatial data consists of points as well as objects that have extent such as line segments, rectangles, regions, and volumes. The points may have locational as well as nonlocational attributes. The focus is on spatial data which is a subset of multidimensional data consisting of points with locational attributes and objects with extent. The emphasis is on hierarchical representations based on the "divide-and-conquer" problem-solving paradigm. They are of interest because they enable focusing computational resources on the interesting subsets of data. Thus, there is no need to expend work where the payoff is small. These representations are of use in operations such as range searching and finding nearest neighbors.