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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 334 (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.
Pad  An Alternative Approach to the Computer Interface
 In Proc. ACM SIGGRAPH
, 1993
"... We believe that navigation in information spaces is best supported by tapping into our natural spatial and geographic ways of thinking. To this end, we are developing a new computer interface model called Pad. The ongoing Pad project uses a spatial metaphor for computer interface design. It provides ..."
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Cited by 328 (2 self)
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We believe that navigation in information spaces is best supported by tapping into our natural spatial and geographic ways of thinking. To this end, we are developing a new computer interface model called Pad. The ongoing Pad project uses a spatial metaphor for computer interface design. It provides an intuitive base for the support of such applications as electronic marketplaces, information services, and online collaboration. Pad is an infinite twodimensional information plane that is shared among users, much as a network file system is shared. Objects are organized geographically; every object occupies a well defined region on the Pad surface. For navigation, Pad uses "portals"  magnifying glasses that can peer into and roam over different parts of this single infinite shared desktop; links to specific items are established and broken continually as the portal's view changes. Portals can recursively look onto other portals. This paradigm enables the sort of peripheral activity generally found in real phy...
Simulation of Simplicity: A Technique to Cope with Degenerate Cases in Geometric Algorithms
 ACM TRANS. GRAPH
, 1990
"... This paper describes a generalpurpose programming technique, called the Simulation of Simplicity, which can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task to provide a consistent treatment for every single special case that can occur. T ..."
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Cited by 317 (23 self)
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This paper describes a generalpurpose programming technique, called the Simulation of Simplicity, which can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task to provide a consistent treatment for every single special case that can occur. The programs that use the technique tend to be considerably smaller and more robust than those that do not use it. We believe that this technique will become a standard tool in writing geometric software.
Efficient Algorithms for Mining Outliers from Large Data Sets
"... In this paper, we propose a novel formulation for distancebased outliers that is based on the distance of a point from its k th nearest neighbor. We rank each point on the basis of its distance to its k th nearest neighbor and declare the top n points in this ranking to be outliers. In addition ..."
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Cited by 316 (1 self)
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In this paper, we propose a novel formulation for distancebased outliers that is based on the distance of a point from its k th nearest neighbor. We rank each point on the basis of its distance to its k th nearest neighbor and declare the top n points in this ranking to be outliers. In addition to developing relatively straightforward solutions to finding such outliers based on the classical nestedloop join and index join algorithms, we develop a highly efficient partitionbased algorithm for mining outliers. This algorithm first partitions the input data set into disjoint subsets, and then prunes entire partitions as soon as it is determined that they cannot contain outliers. This results in substantial savings in computation. We present the results of an extensive experimental study on reallife and synthetic data sets. The results from a reallife NBA database highlight and reveal several expected and unexpected aspects of the database. The results from a study on synthetic data sets demonstrate that the partitionbased algorithm scales well with respect to both data set size and data set dimensionality. 1
A Weighted Nearest Neighbor Algorithm for Learning with Symbolic Features
 Machine Learning
, 1993
"... In the past, nearest neighbor algorithms for learning from examples have worked best in domains in which all features had numeric values. In such domains, the examples can be treated as points and distance metrics can use standard definitions. In symbolic domains, a more sophisticated treatment of t ..."
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Cited by 305 (3 self)
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In the past, nearest neighbor algorithms for learning from examples have worked best in domains in which all features had numeric values. In such domains, the examples can be treated as points and distance metrics can use standard definitions. In symbolic domains, a more sophisticated treatment of the feature space is required. We introduce a nearest neighbor algorithm for learning in domains with symbolic features. Our algorithm calculates distance tables that allow it to produce realvalued distances between instances, and attaches weights to the instances to further modify the structure of feature space. We show that this technique produces excellent classification accuracy on three problems that have been studied by machine learning researchers: predicting protein secondary structure, identifying DNA promoter sequences, and pronouncing English text. Direct experimental comparisons with the other learning algorithms show that our nearest neighbor algorithm is comparable or superior ...
Approximation Algorithms for Projective Clustering
 Proceedings of the ACM SIGMOD International Conference on Management of data, Philadelphia
, 2000
"... We consider the following two instances of the projective clustering problem: Given a set S of n points in R d and an integer k ? 0; cover S by k hyperstrips (resp. hypercylinders) so that the maximum width of a hyperstrip (resp., the maximum diameter of a hypercylinder) is minimized. Let w ..."
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Cited by 303 (21 self)
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We consider the following two instances of the projective clustering problem: Given a set S of n points in R d and an integer k ? 0; cover S by k hyperstrips (resp. hypercylinders) so that the maximum width of a hyperstrip (resp., the maximum diameter of a hypercylinder) is minimized. Let w be the smallest value so that S can be covered by k hyperstrips (resp. hypercylinders), each of width (resp. diameter) at most w : In the plane, the two problems are equivalent. It is NPHard to compute k planar strips of width even at most Cw ; for any constant C ? 0 [50]. This paper contains four main results related to projective clustering: (i) For d = 2, we present a randomized algorithm that computes O(k log k) strips of width at most 6w that cover S. Its expected running time is O(nk 2 log 4 n) if k 2 log k n; it also works for larger values of k, but then the expected running time is O(n 2=3 k 8=3 log 4 n). We also propose another algorithm that computes a c...
Efficient collision detection using bounding volume hierarchies of kdops
 IEEE Transactions on Visualization and Computer Graphics
, 1998
"... Abstract—Collision detection is of paramount importance for many applications in computer graphics and visualization. Typically, the input to a collision detection algorithm is a large number of geometric objects comprising an environment, together with a set of objects moving within the environment ..."
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Cited by 289 (4 self)
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Abstract—Collision detection is of paramount importance for many applications in computer graphics and visualization. Typically, the input to a collision detection algorithm is a large number of geometric objects comprising an environment, together with a set of objects moving within the environment. In addition to determining accurately the contacts that occur between pairs of objects, one needs also to do so at realtime rates. Applications such as haptic forcefeedback can require over 1,000 collision queries per second. In this paper, we develop and analyze a method, based on boundingvolume hierarchies, for efficient collision detection for objects moving within highly complex environments. Our choice of bounding volume is to use a “discrete orientation polytope” (“kdop”), a convex polytope whose facets are determined by halfspaces whose outward normals come from a small fixed set of k orientations. We compare a variety of methods for constructing hierarchies (“BVtrees”) of bounding kdops. Further, we propose algorithms for maintaining an effective BVtree of kdops for moving objects, as they rotate, and for performing fast collision detection using BVtrees of the moving objects and of the environment. Our algorithms have been implemented and tested. We provide experimental evidence showing that our approach yields substantially faster collision detection than previous methods. Index Terms—Collision detection, intersection searching, bounding volume hierarchies, discrete orientation polytopes, bounding boxes, virtual reality, virtual environments. 1
A Decomposition of MultiDimensional Point Sets with Applications to kNearestNeighbors and nBody Potential Fields
 J. ACM
, 1992
"... We define the notion of a wellseparated pair decomposition of points in ddimensional space. We then develop efficient sequential and parallel algorithms for computing such a decomposition. We apply the resulting decomposition to the efficient computation of knearest neighbors and nbody potential ..."
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Cited by 281 (4 self)
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We define the notion of a wellseparated pair decomposition of points in ddimensional space. We then develop efficient sequential and parallel algorithms for computing such a decomposition. We apply the resulting decomposition to the efficient computation of knearest neighbors and nbody potential fields.
Shooting Stars in the Sky: An Online Algorithm for Skyline Queries
 In VLDB
, 2002
"... Skyline queries ask for a set of interesting points from a potentially large set of data points. If we are traveling, for instance, a restaurant might be interesting if there is no other restaurant which is nearer, cheaper, and has better food. Skyline queries retrieve all such interesting restauran ..."
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Cited by 280 (0 self)
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Skyline queries ask for a set of interesting points from a potentially large set of data points. If we are traveling, for instance, a restaurant might be interesting if there is no other restaurant which is nearer, cheaper, and has better food. Skyline queries retrieve all such interesting restaurants so that the user can choose the most promising one. In this paper, we present a new online algorithm that computes the Skyline. Unlike most existing algorithms that compute the Skyline in a batch, this algorithm returns the first results immediately, produces more and more results continuously, and allows the user to give preferences during the running time of the algorithm so that the user can control what kind of results are produced next (e.g., rather cheap or rather near restaurants).
Data structures for mobile data
 JOURNAL OF ALGORITHMS
, 1997
"... A kinetic data structure (KDS) maintains an attribute of interest in a system of geometric objects undergoing continuous motion. In this paper we develop a conceptual framework for kinetic data structures, propose a number of criteria for the quality of such structures, and describe a number of fund ..."
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Cited by 270 (57 self)
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A kinetic data structure (KDS) maintains an attribute of interest in a system of geometric objects undergoing continuous motion. In this paper we develop a conceptual framework for kinetic data structures, propose a number of criteria for the quality of such structures, and describe a number of fundamental techniques for their design. We illustrate these general concepts by presenting kinetic data structures for maintaining the convex hull and the closest pair of moving points in the plane; these structures behavewell according to the proposed quality criteria for KDSs.