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SIGMOD '86 Proceedings of the 1986 ACM SIGMOD international conference on Management of data
A formula for computing the number of quadtree node fragments created by a shift
Pattern Recognition Letters
Gray Codes for Partial Match and Range Queries
IEEE Transactions on Software Engineering
Fractals for secondary key retrieval
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Linear clustering of objects with multiple attributes
SIGMOD '90 Proceedings of the 1990 ACM SIGMOD international conference on Management of data
Segment indexes: dynamic indexing techniques for multi-dimensional interval data
SIGMOD '91 Proceedings of the 1991 ACM SIGMOD international conference on Management of data
Analysis of the clustering of Peano curves
Analysis of the clustering of Peano curves
Analytical results on the quadtree decomposition of arbitrary rectangles
Pattern Recognition Letters
Multidimensional binary search trees used for associative searching
Communications of the ACM
Computer Vision
PROBE Spatial Data Modeling and Query Processing in an Image Database Application
IEEE Transactions on Software Engineering
DOT: A Spatial Access Method Using Fractals
Proceedings of the Seventh International Conference on Data Engineering
QBISM: Extending a DBMS to Support 3D Medical Images
Proceedings of the Tenth International Conference on Data Engineering
Optimization for Spatial Query Processing
VLDB '91 Proceedings of the 17th International Conference on Very Large Data Bases
Proceedings of the Sixth International Conference on Data Engineering
Snakes and sandwiches: optimal clustering strategies for a data warehouse
SIGMOD '99 Proceedings of the 1999 ACM SIGMOD international conference on Management of data
Design and analysis of data structures for querying image databases
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SP-GiST: An Extensible Database Index for Supporting Space Partitioning Trees
Journal of Intelligent Information Systems
Analysis of the Clustering Properties of the Hilbert Space-Filling Curve
IEEE Transactions on Knowledge and Data Engineering
Analysis of n-Dimensional Quadtrees using the Hausdorff Fractal Dimension
VLDB '96 Proceedings of the 22th International Conference on Very Large Data Bases
S*-Tree: An Improved S+-Tree for Coloured Images
ADBIS '99 Proceedings of the Third East European Conference on Advances in Databases and Information Systems
Interval Sequences: An Object-Relational Approach to Manage Spatial Data
SSTD '01 Proceedings of the 7th International Symposium on Advances in Spatial and Temporal Databases
IEEE Transactions on Knowledge and Data Engineering
Object-relational management of complex geographical objects
Proceedings of the 12th annual ACM international workshop on Geographic information systems
An Exact Closed-Form Formula for d-Dimensional Quadtree Decomposition of Arbitrary Hyperrectangles
IEEE Transactions on Knowledge and Data Engineering
Twins: A Dual Addressing Space Representation for Self-Organizing Networks
IEEE Transactions on Parallel and Distributed Systems
Color PCA eigenimages and their application to compression and watermarking
Image and Vision Computing
ICAI'05/MCBC'05/AMTA'05/MCBE'05 Proceedings of the 6th WSEAS international conference on Automation & information, and 6th WSEAS international conference on mathematics and computers in biology and chemistry, and 6th WSEAS international conference on acoustics and music: theory and applications, and 6th WSEAS international conference on Mathematics and computers in business and economics
Multiresolution query optimization in an online environment
APWeb'05 Proceedings of the 7th Asia-Pacific web conference on Web Technologies Research and Development
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We give a closed-form expression for the average number of n-dimensional quadtree nodes ("pieces" or "blocks") required by an n-dimensional hyperrectangle aligned with the axes. Our formula includes as special cases the formulae of previous efforts for two-dimensional spaces [8]. It also agrees with theoretical and empirical results that the number of blocks depends on the hypersurface of the hyperrectangle and not on its hypervolume. The practical use of the derived formula is that it allows the estimation of the space requirements of the n-dimensional quadtree decomposition. Quadtrees are used extensively in two-dimensional spaces (geographic information systems and spatial databases in general), as well in higher dimensionality spaces (as oct-trees for three-dimensional spaces, e.g., in graphics, robotics, and three-dimensional medical images [2]). Our formula permits the estimation of the space requirements for data hyperrectangles when stored in an index structure like a (n-dimensional) quadtree, as well as the estimation of the search time for query hyperrectangles, for the so-called linear quadtrees [17]. A theoretical contribution of the paper is the observation that the number of blocks is a piece-wise linear function of the sides of the hyperrectangle.