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24
Multidimensional Access Methods
, 1998
"... Search operations in databases require special support at the physical level. This is true for conventional databases as well as spatial databases, where typical search operations include the point query (find all objects that contain a given search point) and the region query (find all objects that ..."
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Cited by 561 (3 self)
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Search operations in databases require special support at the physical level. This is true for conventional databases as well as spatial databases, where typical search operations include the point query (find all objects that contain a given search point) and the region query (find all objects that overlap a given search region). More
The quadtree and related hierarchical data structures
 ACM Computing Surveys
, 1984
"... A tutorial survey is presented of the quadtree and related hierarchical data structures. They are based on the principle of recursive decomposition. The emphasis is on the representation of data used in applications in image processing, computer graphics, geographic information systems, and robotics ..."
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Cited by 421 (11 self)
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A tutorial survey is presented of the quadtree and related hierarchical data structures. They are based on the principle of recursive decomposition. The emphasis is on the representation of data used in applications in image processing, computer graphics, geographic information systems, and robotics. There is a greater emphasis on region data (i.e., twodimensional shapes) and to a lesser extent on point, curvilinear, and threedimensional data. A number of operations in which such data structures find use are examined in greater detail.
Spatial Data Structures
, 1995
"... An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarch ..."
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Cited by 287 (13 self)
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An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarchical data structures are based on the principle of recursive decomposition. They are attractive because they are compact and depending on the nature of the data they save space as well as time and also facilitate operations such as search. Examples are given of the use of these data structures in the representation of different data types such as regions, points, rectangles, lines, and volumes.
Navigating through Triangle Meshes Implemented as Linear Quadtrees
 ACM Transactions on Graphics
, 1998
"... Techniques are presented for navigating between adjacent triangles of greater or equal size in a hierarchical triangle mesh where the triangles are obtained by a recursive quadtreelike subdivision of the underlying space into four equilateral triangles. These techniques are useful in a number of ap ..."
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Cited by 28 (1 self)
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Techniques are presented for navigating between adjacent triangles of greater or equal size in a hierarchical triangle mesh where the triangles are obtained by a recursive quadtreelike subdivision of the underlying space into four equilateral triangles. These techniques are useful in a number of applications including finite element analysis, ray tracing, and the modeling of spherical data. The operations are implemented in a manner analogous to that used in a quadtree representation of data on the twodimensional plane where the underlying space is tessellated into a square mesh. A new technique is described for labeling the triangles which is useful in implementing the quadtree triangle mesh as a linear quadtree (i.e., a pointerless quadtree); the navigation can then take place in this linear quadtree. When the neighbors are of equal size, the algorithms take constant time. The algorithms are very efficient, as they make use of just a few bit manipulation operations and can be impl...
Hierarchical representations of collections of small rectangles
 ACM Computing Surveys
, 1988
"... A tutorial survey is presented of hierarchical data structures for representing collections of small rectangles. Rectangles are often used as an approximation of shapes for which they serve as the minimum rectilinear enclosing object. They arise in applications in cartography as well as very larges ..."
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Cited by 24 (1 self)
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A tutorial survey is presented of hierarchical data structures for representing collections of small rectangles. Rectangles are often used as an approximation of shapes for which they serve as the minimum rectilinear enclosing object. They arise in applications in cartography as well as very largescale integration (VLSI) design rule checking. The different data structures are discussed in terms of how they support the execution of queries involving proximity relations. The focus is on intersection and subset queries. Several types of representations are described. Some are designed for use with the planesweep paradigm, which works well for static collections of rectangles. Others are oriented toward dynamic collections. In this case, one representation reduces each rectangle to a point in a higher multidimensional space and treats the problem as one involving point data. The other representation is area basedthat is, it depends on the physical extent of each rectangle.
Analysis of ndimensional Quadtrees Using the Hausdorff Fractal Dimension
 In Proc. 22nd Int. Conf. on Very Large Data Bases
, 1996
"... There is mounting evidence [Man77, Sch91] that real datasets are statistically selfsimilar, and thus, `fractal'. This is an important insight since it permits a compact statistical description of spatial datasets; subsequently, as we show, it also forms the basis for the theoretical analysis of spa ..."
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Cited by 20 (2 self)
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There is mounting evidence [Man77, Sch91] that real datasets are statistically selfsimilar, and thus, `fractal'. This is an important insight since it permits a compact statistical description of spatial datasets; subsequently, as we show, it also forms the basis for the theoretical analysis of spatial access methods, without using the typical, but unrealistic, uniformity assumption. In this paper, we focus on the estimation of the number of quadtree blocks that a real, spatial dataset will require. Using the the wellknown Hausdorff fractal dimension, we derive some closed formulas which allow us to predict the number of quadtree blocks, given some few parameters. Using our formulas, it is possible to predict the space overhead and the response time of linear quadtrees/zordering [OM88], which are widely used in practice. In order to verify our analytical model, we performed an extensive experimental investigation using several real datasets coming from different domains. In these ex...
Spgist: An extensible database index for supporting space partitioning trees
 J. Intell. Inf. Syst
"... Abstract. Emerging database applications require the use of new indexing structures beyond Btrees and Rtrees. Examples are the kD tree, the trie, the quadtree, and their variants. They are often proposed as supporting structures in data mining, GIS, and CAD/CAM applications. A common feature of a ..."
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Cited by 20 (8 self)
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Abstract. Emerging database applications require the use of new indexing structures beyond Btrees and Rtrees. Examples are the kD tree, the trie, the quadtree, and their variants. They are often proposed as supporting structures in data mining, GIS, and CAD/CAM applications. A common feature of all these indexes is that they recursively divide the space into partitions. A new extensible index structure, termed SPGiST is presented that supports this class of data structures, mainly the class of space partitioning unbalanced trees. Simple method implementations are provided that demonstrate how SPGiST can behave as a kD tree, a trie, a quadtree, or any of their variants. Issues related to clustering tree nodes into pages as well as concurrency control for SPGiST are addressed. A dynamic minimumheight clustering technique is applied to minimize disk accesses and to make using such trees in database systems possible and efficient. A prototype implementation of SPGiST is presented as well as performance studies of the various SPGiST’s tuning parameters. Keywords: spacepartitioning trees, spatial databases, extensible index, generalized search trees, clustering
Scalebased Clustering using the Radial Basis Function Network
 IEEE Trans. Neural Networks
, 1996
"... This paper shows how scalebased clustering can be done using the Radial Basis Function (RBF) Network, with the RBF width as the scale parameter and a dummy target as the desired output. The technique suggests the "right" scale at which the given data set should be clustered, thereby providing a sol ..."
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Cited by 17 (3 self)
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This paper shows how scalebased clustering can be done using the Radial Basis Function (RBF) Network, with the RBF width as the scale parameter and a dummy target as the desired output. The technique suggests the "right" scale at which the given data set should be clustered, thereby providing a solution to the problem of determining the number of RBF units and the widths required to get a good network solution. The network compares favorably with other standard techniques on benchmark clustering examples. Properties that are required of nongaussian basis functions, if they are to serve in alternative clustering networks, are identified. The work on the whole points out an important role played by the width parameter in RBFN, when observed over several scales, and provides a fundamental link to the scale space theory developed in computational vision. The work described here is supported in part by the National Science Foundation under grant ECS9307632 and in part by ONR Contract N...
Spatial Join Techniques
"... A variety of techniques for performing a spatial join are reviewed. Instead of just summarizing the literature and presenting each technique in its entirety, distinct components of the different techniques are described and each is decomposed into an overall framework for performing a spatial join. ..."
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Cited by 17 (3 self)
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A variety of techniques for performing a spatial join are reviewed. Instead of just summarizing the literature and presenting each technique in its entirety, distinct components of the different techniques are described and each is decomposed into an overall framework for performing a spatial join. A typical spatial join technique consists of the following components: partitioning the data, performing internalmemory spatial joins on subsets of the data, and checking if the full polygons intersect. Each technique is decomposed into these components and each component addressed in a separate section so as to compare and contrast similar aspects of each technique. The goal of this survey is to describe the algorithms within each component in detail, comparing and contrasting competing methods, thereby enabling further analysis and experimentation with each component and allowing the best algorithms for a particular situation to be built piecemeal, or, even better, enabling an optimizer to choose which algorithms to use. Categories and Subject Descriptors: H.2.4 [Database Management]: Systems—Query processing; H.2.8 [Database Management]: Database Applications—Spatial databases and GIS
Hashing by proximity to process duplicates in spatial databases
 In Proceedings of the 3rd International Conference on Information and Knowledge Management (CIKM
, 1994
"... In a spatial database, an object may extend arbitrarily in space. As a result, many spatial data structures (e.g., the quadtree, the cell tree, the R +tree) represent an object by partitioning it into multiple, yet simple, pieces, each of which is stored separately inside the data structure. Many o ..."
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Cited by 11 (7 self)
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In a spatial database, an object may extend arbitrarily in space. As a result, many spatial data structures (e.g., the quadtree, the cell tree, the R +tree) represent an object by partitioning it into multiple, yet simple, pieces, each of which is stored separately inside the data structure. Many operations on these data structures are likely to produce duplicate results because of the multiplicity of object pieces. A novel approach for duplicate processing based on proximity of spatial objects is presented. This is di erent from conventional duplicate elimination in database systems because, with spatial databases, di erent pieces of the same object can span multiple buckets of the underlying data structure. Example algorithms are presented to perform duplicate processing using proximity for a quadtree representation of line segments and arbitrary rectangles. The complexity of the algorithms is seen to depend on a geometric classi cation of di erent instances of the spatial objects. By using proximity and the spatial properties of the objects, the number of diskI/O requests as well as the runtime storage during duplicate processing can be reduced. 1