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Approximate distance oracles
 J. ACM
"... Let G = (V, E) be an undirected weighted graph with V  = n and E  = m. Let k ≥ 1 be an integer. We show that G = (V, E) can be preprocessed in O(kmn 1/k) expected time, constructing a data structure of size O(kn 1+1/k), such that any subsequent distance query can be answered, approximately, in ..."
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Cited by 279 (10 self)
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Let G = (V, E) be an undirected weighted graph with V  = n and E  = m. Let k ≥ 1 be an integer. We show that G = (V, E) can be preprocessed in O(kmn 1/k) expected time, constructing a data structure of size O(kn 1+1/k), such that any subsequent distance query can be answered, approximately
Approximate Distance Labeling Schemes
, 2000
"... We consider the problem of labeling the nodes of an nnode graph G with short labels in such a way that the distance between any two nodes u; v of G can be approximated eciently (in constant time) by merely inspecting the labels of u and v, without using any other information. We develop such con ..."
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Cited by 47 (18 self)
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We consider the problem of labeling the nodes of an nnode graph G with short labels in such a way that the distance between any two nodes u; v of G can be approximated eciently (in constant time) by merely inspecting the labels of u and v, without using any other information. We develop
The case for approximate Distance Transforms
"... Starting with a binary raster, the calculation of exact Euclidean distance from the foreground pixels (1elements) to the background pixels (0elements) is a simple yet timeconsuming operation. Elsewhere it is argued that for some applications (such as pattern recognition and robotics for example) ..."
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Cited by 2 (0 self)
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) the calculation of approximate Euclidean distance is a viable, quick and efficient alternative solution. There has been much research on a number of innovative approximate distance transforms. The vast majority of these have been reported in the computer science and mathematical literature, and yet given its
Approximate distance oracles for unweighted graphs . . .
"... ������������ � Let be an undirected graph � on vertices, and ���������� � let denote the distance � in between two � vertices � and. Thorup and Zwick showed that for any +ve � integer, the � graph can be preprocessed to build a datastructure that can efficiently � reportapproximate distance betwee ..."
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Cited by 58 (10 self)
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������������ � Let be an undirected graph � on vertices, and ���������� � let denote the distance � in between two � vertices � and. Thorup and Zwick showed that for any +ve � integer, the � graph can be preprocessed to build a datastructure that can efficiently � reportapproximate distance
Approximate Distance Oracles Revisited
, 2002
"... Let G be a geometric tspanner in E with n points and m edges, where t is a constant. We show that G can be preprocessed in O(m log n) time, such that (1+")approximate shortestpath queries in G can be answered in O(1) time. The data structure uses O(n log n) space. ..."
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Cited by 8 (4 self)
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Let G be a geometric tspanner in E with n points and m edges, where t is a constant. We show that G can be preprocessed in O(m log n) time, such that (1+")approximate shortestpath queries in G can be answered in O(1) time. The data structure uses O(n log n) space.
Approximate Distance Classification
 In Computer Science and Statistics, Proceedings of the 30th Symposium on the Interface
, 1998
"... We investigate the use of a class of nonlinear projections from a highdimensional Euclidean space to a lowdimensional space in a classification (supervised learning) context. The projections developed by Cowen and Priebe approximately preserve interclass distances. Projected data was obtained from ..."
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We investigate the use of a class of nonlinear projections from a highdimensional Euclidean space to a lowdimensional space in a classification (supervised learning) context. The projections developed by Cowen and Priebe approximately preserve interclass distances. Projected data was obtained from
Exact and Approximate Distances in Graphs  a survey
 In ESA
, 2001
"... We survey recent and not so recent results related to the computation of exact and approximate distances, and corresponding shortest, or almost shortest, paths in graphs. We consider many different settings and models and try to identify some remaining open problems. ..."
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Cited by 70 (0 self)
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We survey recent and not so recent results related to the computation of exact and approximate distances, and corresponding shortest, or almost shortest, paths in graphs. We consider many different settings and models and try to identify some remaining open problems.
Approximate distance oracles for geometric spanners
 Submitted
, 2002
"... Given an arbitrary real constant ε> 0, and a geometric graph G in ddimensional Euclidean space with n points, O(n) edges, and constant dilation, our main result is a data structure that answers (1 + ε)approximate shortest path length queries in constant time. The data structure can be construct ..."
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Cited by 13 (2 self)
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be constructed in O(n log n) time using O(n log n) space. This represents the first data structure that answers (1 + ε)approximate shortest path queries in constant time, and hence functions as an approximate distance oracle. The data structure is also applied to several other problems. In particular, we also
Approximate Distance Oracles for Geometric Graphs
, 2002
"... Given a geometric tspanner graph G in E d with n points and m edges, with edge lengths that lie within a polynomial (in n) factor of each other. Then, after O(m+n log n) preprocessing, we present an approximation scheme to answer (1+") approximate shortest path queries in O(1) time. The dat ..."
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Cited by 37 (11 self)
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Given a geometric tspanner graph G in E d with n points and m edges, with edge lengths that lie within a polynomial (in n) factor of each other. Then, after O(m+n log n) preprocessing, we present an approximation scheme to answer (1+") approximate shortest path queries in O(1) time
Approximate distance queries in disk graphs
 In WAOA ’06 (2006
"... We present efficient algorithms for approximately answering distance queries in disk graphs. Let G be a disk graph with n vertices and m edges. For any fixed ǫ> 0, we show that G can be preprocessed in O(m √ nǫ −1 + mǫ −2 log S) time, constructing a data structure of size O(n 3/2 ǫ −1 + nǫ −2 log ..."
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Cited by 3 (2 self)
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We present efficient algorithms for approximately answering distance queries in disk graphs. Let G be a disk graph with n vertices and m edges. For any fixed ǫ> 0, we show that G can be preprocessed in O(m √ nǫ −1 + mǫ −2 log S) time, constructing a data structure of size O(n 3/2 ǫ −1 + nǫ −2
Results 1  10
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1,444,676