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On constructing minimum spanning trees in kdimensional space and related problems
 SIAM JOURNAL ON COMPUTING
, 1982
"... . The problem of finding a minimum spanning tree connecting n points in a kdimensional space is discussed under three common distance metrics: Euclidean, rectilinear, and L. By employing a subroutine that solves the post office problem, we show that, for fixed k _> 3, such a minimum spanning t ..."
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Cited by 222 (1 self)
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. The problem of finding a minimum spanning tree connecting n points in a kdimensional space is discussed under three common distance metrics: Euclidean, rectilinear, and L. By employing a subroutine that solves the post office problem, we show that, for fixed k _> 3, such a minimum spanning
Fastmap: A fast algorithm for indexing, datamining and visualization of traditional and multimedia datasets
, 1995
"... A very promising idea for fast searching in traditional and multimedia databases is to map objects into points in kd space, using k featureextraction functions, provided by a domain expert [Jag91]. Thus, we can subsequently use highly finetuned spatial access methods (SAMs), to answer several ..."
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Cited by 502 (22 self)
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easier for a domain expert to assess the similarity/distance of two objects. Given only the distance information though, it is not obvious how to map objects into points. This is exactly the topic of this paper. We describe a fast algorithm to map objects into points in some kdimensional space (k
Tree visualization with Treemaps: A 2d spacefilling approach
 ACM Transactions on Graphics
, 1991
"... this paper deals with a twodimensional (2d) spacefilling approach in which each node is a rectangle whose area is proportional to some attribute such as node size. Research on relationships between 2d images and their representation in tree structures has focussed on node and link representation ..."
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Cited by 534 (29 self)
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this paper deals with a twodimensional (2d) spacefilling approach in which each node is a rectangle whose area is proportional to some attribute such as node size. Research on relationships between 2d images and their representation in tree structures has focussed on node and link
Refinements to NearestNeighbor Searching in kDimensional Trees
 ALGORITHMICA
, 1991
"... This note presents a simplification and generalization of an algorithm for searching kdimensional trees for nearest neighbors reported by Friedman et al. I3]. If the distance between records is measured using Lz, the Euclidean orm, the data structure used by the algorithm to determine the bounds ..."
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Cited by 123 (0 self)
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This note presents a simplification and generalization of an algorithm for searching kdimensional trees for nearest neighbors reported by Friedman et al. I3]. If the distance between records is measured using Lz, the Euclidean orm, the data structure used by the algorithm to determine the bounds
An Optimal Algorithm for Approximate Nearest Neighbor Searching in Fixed Dimensions
 ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 1994
"... Consider a set S of n data points in real ddimensional space, R d , where distances are measured using any Minkowski metric. In nearest neighbor searching we preprocess S into a data structure, so that given any query point q 2 R d , the closest point of S to q can be reported quickly. Given any po ..."
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Cited by 984 (32 self)
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Consider a set S of n data points in real ddimensional space, R d , where distances are measured using any Minkowski metric. In nearest neighbor searching we preprocess S into a data structure, so that given any query point q 2 R d , the closest point of S to q can be reported quickly. Given any
Fast approximate nearest neighbors with automatic algorithm configuration
 In VISAPP International Conference on Computer Vision Theory and Applications
, 2009
"... nearestneighbors search, randomized kdtrees, hierarchical kmeans tree, clustering. For many computer vision problems, the most time consuming component consists of nearest neighbor matching in highdimensional spaces. There are no known exact algorithms for solving these highdimensional problems ..."
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Cited by 455 (2 self)
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nearestneighbors search, randomized kdtrees, hierarchical kmeans tree, clustering. For many computer vision problems, the most time consuming component consists of nearest neighbor matching in highdimensional spaces. There are no known exact algorithms for solving these highdimensional
A New Way to Weigh Malnourished Euclidean Graphs
"... In this paper, we show that any Euclidean graph over a set V of n points in kdimensional space that satisfies either the leapfrog property or the isolation property has small weight, i.e., has weight O(1). wt(SMT), where SMT is a Steiner minimal tree of V. Both the leapfrog property as well as the ..."
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Cited by 43 (2 self)
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In this paper, we show that any Euclidean graph over a set V of n points in kdimensional space that satisfies either the leapfrog property or the isolation property has small weight, i.e., has weight O(1). wt(SMT), where SMT is a Steiner minimal tree of V. Both the leapfrog property as well
A Ramseytype bound for rectangles
"... It is proved that for any rectangle T and for any 2coloring of the points of the 5dimensional Euclidean space, one can always nd a rectangle T congruent to T , all of whose vertices are of the same color. We also show that for any kcoloring of the k ){dimensional space, there is a m ..."
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It is proved that for any rectangle T and for any 2coloring of the points of the 5dimensional Euclidean space, one can always nd a rectangle T congruent to T , all of whose vertices are of the same color. We also show that for any kcoloring of the k ){dimensional space, there is a
Results 1  10
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4,412