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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 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 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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distance query in constant time. They named the datastructure “oracle ” because of this feature. Furthermore the tradeoff between � stretch and the size of the datastructure is essentially optimal. In this paper we show that we can actually construct approximate distance oracles in ��������� expected
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 oracles with improved query time
 MATHEMATICS AND COMPUTER SCIENCE DEPARTMENT, OPEN UNIVERSITY OF ISRAEL
, 2011
"... Given an undirected graph G with m edges, n vertices, and nonnegative edge weights, and given an integer k ≥ 1, we show that for some universal constant c, a (2k − 1)approximate distance oracle for G of size O(kn 1+1/k) can be constructed in O ( √ km+kn 1+c/ √ k) time and can answer queries in O(k ..."
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Cited by 12 (1 self)
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Given an undirected graph G with m edges, n vertices, and nonnegative edge weights, and given an integer k ≥ 1, we show that for some universal constant c, a (2k − 1)approximate distance oracle for G of size O(kn 1+1/k) can be constructed in O ( √ km+kn 1+c/ √ k) time and can answer queries in O
6.889 — Lecture 13: Approximate Distance Oracles
, 2011
"... Approximate Distance Oracle: given a graph G = (V,E), preprocess it into a data structure such that we can compute approximate shortestpath distances efficiently (and output path if desired). (same scenario as in Lecture 12 except that paths are allowed to be approximately shortest) Assumption (all ..."
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Approximate Distance Oracle: given a graph G = (V,E), preprocess it into a data structure such that we can compute approximate shortestpath distances efficiently (and output path if desired). (same scenario as in Lecture 12 except that paths are allowed to be approximately shortest) Assumption
Approximate Distance Oracles for Graphs with Dense Clusters
"... Abstract. Let H1 = (V, F1) be a collection of N pairwise vertex disjoint O(1)spanners where the weight of an edge is equal to the Euclidean distance between its endpoints. Let H2 = (V, F2) be a graph on V with M edges of nonnegative weight. The union of the two graphs is denoted G = (V, F1 ∪ F2). ..."
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Cited by 1 (0 self)
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Abstract. Let H1 = (V, F1) be a collection of N pairwise vertex disjoint O(1)spanners where the weight of an edge is equal to the Euclidean distance between its endpoints. Let H2 = (V, F2) be a graph on V with M edges of nonnegative weight. The union of the two graphs is denoted G = (V, F1 ∪ F2
Results 1  10
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1,481,942