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LowDistortion Embeddings of Trees
 Journal of Graph Algorithms and Applications
, 2003
"... We prove that every tree T = (V,E) on n vertices with edges of unit length can be embedded in the plane with distortion O( n); that is, we construct a mapping f : V > R² such that #(u, v) f(v) O( n) #(u, v) for every u, v V ,where#(u, v) denotes the length of the path from u to v in T ..."
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Cited by 10 (1 self)
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We prove that every tree T = (V,E) on n vertices with edges of unit length can be embedded in the plane with distortion O( n); that is, we construct a mapping f : V > R² such that #(u, v) f(v) O( n) #(u, v) for every u, v V ,where#(u, v) denotes the length of the path from u to v
Low distortion embeddings for edit distance
 In Proceedings of the Symposium on Theory of Computing
, 2005
"... We show that {0, 1} d endowed with edit distance embeds into ℓ1 with distortion 2 O( √ log d log log d). We further show efficient implementations of the embedding that yield solutions to various computational problems involving edit distance. These include sketching, communication complexity, neare ..."
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Cited by 26 (1 self)
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We show that {0, 1} d endowed with edit distance embeds into ℓ1 with distortion 2 O( √ log d log log d). We further show efficient implementations of the embedding that yield solutions to various computational problems involving edit distance. These include sketching, communication complexity
Bounded geometries, fractals, and lowdistortion embeddings
"... The doubling constant of a metric space (X; d) is thesmallest value * such that every ball in X can be covered by * balls of half the radius. The doubling dimension of X isthen defined as dim(X) = log2 *. A metric (or sequence ofmetrics) is called doubling precisely when its doubling dimension is ..."
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Cited by 198 (40 self)
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is bounded. This is a robust class of metric spaceswhich contains many families of metrics that occur in applied settings.We give tight bounds for embedding doubling metrics into (lowdimensional) normed spaces. We consider bothgeneral doubling metrics, as well as more restricted families such as those
Lowdistortion embeddings of general metrics into the line
 In STOC’05: Proceedings of the 37th Annual ACM Symposium on Theory of Computing
, 2005
"... A lowdistortion embedding between two metric spaces is a mapping which preserves the distances between each pair of points, up to a small factor called distortion. Lowdistortion embeddings have recently found numerous applications in computer science. Most of the known embedding results are ”absol ..."
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Cited by 25 (8 self)
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A lowdistortion embedding between two metric spaces is a mapping which preserves the distances between each pair of points, up to a small factor called distortion. Lowdistortion embeddings have recently found numerous applications in computer science. Most of the known embedding results
LowDistortion Embeddings of Finite Metric Spaces
 in Handbook of Discrete and Computational Geometry
, 2004
"... INTRODUCTION An npoint metric space (X; D) can be represented by an n n table specifying the distances. Such tables arise in many diverse areas. For example, consider the following scenario in microbiology: X is a collection of bacterial strains, and for every two strains, one is given their diss ..."
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Cited by 63 (1 self)
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INTRODUCTION An npoint metric space (X; D) can be represented by an n n table specifying the distances. Such tables arise in many diverse areas. For example, consider the following scenario in microbiology: X is a collection of bacterial strains, and for every two strains, one is given their dissimilarity (computed, say, by comparing their DNA). It is dicult to see any structure in a large table of numbers, and so we would like to represent a given metric space in a more comprehensible way. For example, it would be very nice if we could assign to each x 2 X a point f(x) in the plane in such a way that D(x; y) equals the Euclidean distance of f(x) and f(y). Such a representation would allow us to see the structure of the metric space: tight clusters, isolated points, and so on. Another advantage would be that the metric would now be represented by only 2n real numbers, the coordinates of the n points in the plane, instead of numbers as before. Moreover, many quantities concern
The complexity of lowdistortion embeddings between point sets
 Proceedings of SODA 2005
, 2005
"... Abstract We prove that it is NPhard to approximate by a ratio better than 3 the minimum distortionof a bijection between two given finite threedimensional sets of points. ..."
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Cited by 17 (1 self)
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Abstract We prove that it is NPhard to approximate by a ratio better than 3 the minimum distortionof a bijection between two given finite threedimensional sets of points.
On Low Distortion Embeddings of Statistical Distance Measures into Low Dimensional Spaces ∗
, 909
"... Statistical distance measures have found wide applicability in information retrieval tasks that typically involve high dimensional datasets. In order to reduce the storage space and ensure efficient performance of queries, dimensionality reduction while preserving the interpoint similarity is highl ..."
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Cited by 2 (0 self)
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is highly desirable. In this paper, we investigate various statistical distance measures from the point of view of discovering low distortion embeddings into lowdimensional spaces. More specifically, we consider the Mahalanobis distance measure, the Bhattacharyya class of divergences and the Kullback
Results 1  10
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