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Approximating Approximate Distance Oracles
[article]

2016
*
arXiv
*
pre-print

Given a finite metric space (V,d), an

arXiv:1612.05623v1
fatcat:yldtsxpkrjbl7ftgd2orszyf64
*approximate**distance**oracle*is a data structure which, when queried on two points u,v ∈ V, returns an*approximation*to the the actual*distance*between u and v which ... In particular, we give an O( n)-*approximation*to the problem of finding the smallest stretch 3 Thorup-Zwick*distance**oracle*, as well as the problem of finding the smallest Pǎtraşcu-Roditty*distance**oracle*... In this paper we ask a natural but very different type of question about*approximate**distance**oracles*: can we find (or*approximate*) the best*approximate**distance**oracle*? ...##
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Approximate distance oracles

2001
*
Proceedings of the thirty-third annual ACM symposium on Theory of computing - STOC '01
*

The

doi:10.1145/380752.380798
dblp:conf/stoc/ThorupZ01
fatcat:wvffmpvwnnc5rfsnx2yljzklli
*approximate**distance*returned is of stretch at most 2k − 1, i.e., the quotient obtained by dividing the estimated*distance*by the actual*distance*lies between 1 and 2k −1. ... 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 ...*oracles*and*distance*labels. ...##
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Approximate distance oracles

2005
*
Journal of the ACM
*

The

doi:10.1145/1044731.1044732
fatcat:fj4vnfij5je3db2wi5aspdbbu4
*approximate**distance*returned is of stretch at most 2k − 1, i.e., the quotient obtained by dividing the estimated*distance*by the actual*distance*lies between 1 and 2k −1. ... 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 ...*oracles*and*distance*labels. ...##
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Approximate Distance Oracles with Improved Query Time
[article]

2012
*
arXiv
*
pre-print

Furthermore, for any $0 < \epsilon \leq 1$, we give an

arXiv:1202.2336v3
fatcat:iwd27w7qsvfkhlay36jcagygb4
*oracle*of size $O(kn^{1 + 1/k})$ that answers $((2 + \epsilon)k)$-*approximate**distance*queries in $O(1/\epsilon)$ time. ... Given an undirected graph $G$ with $m$ edges, $n$ vertices, and non-negative edge weights, and given an integer $k\geq 2$, we show that a $(2k-1)$-*approximate**distance**oracle*for $G$ of size $O(kn^{1 + ... To our knowledge, the*oracle*of Mendel and Naor cannot be used to produce*approximate*shortest paths, only*distances*. Our second*oracle*then has the same drawback (due to Lemma 10). ...##
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Approximate distance oracles for geometric spanners

2008
*
ACM Transactions on Algorithms
*

This represents the first data structure that answers (1 + ε)-

doi:10.1145/1328911.1328921
fatcat:icaqazphnndw5ijlrxbno772da
*approximate*shortest path queries in constant time, and hence functions as an*approximate**distance**oracle*. ... Other applications include query versions of closest pair problems, and the efficient computation of the*approximate*dilations of geometric graphs. ... Since the query time is essentially bounded by a constant, Thorup and Zwick refer to their queries as*approximate**distance**oracles*. ...##
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More Compact Oracles for Approximate Distances in Planar Graphs
[article]

2011
*
arXiv
*
pre-print

In FOCS'01, Thorup introduced

arXiv:1109.2641v2
fatcat:ghbbqnpzazb25cpu74pdqdoty4
*approximate**distance**oracles*for planar graphs. ...*Distance**oracles*are data structures that provide fast (possibly*approximate*) answers to shortest-path and*distance*queries in graphs. ... Theorem 3 (Additive-Stretch*Approximate**Distance**Oracle*). ...##
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Approximate Distance Oracles Subject to Multiple Vertex Failures
[article]

2020
*
arXiv
*
pre-print

Previously there are (1+ϵ)-

arXiv:2002.06812v2
fatcat:g7cw5tacfjarxb7mep7vkenenm
*approximate*d-edge sensitive*distance**oracles*[Chechik et al. 2017] answering*distance*queries when d edges fail, which have size O(n^2(log n/ϵ)^d· dlog W) and query time poly ... These results are the first*approximate**distance**oracles*of poly-logarithmic query time for any constant number of vertex failures in general undirected graphs. ... Acknowledgments We are grateful to anonymous reviewers for helpful comments, bringing [59] to our attention, and pointing out the recent work [48] that allows us to derandomize the*oracle*in Section ...##
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Approximate Distance Oracle with Constant Query Time
[article]

2013
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arXiv
*
pre-print

An

arXiv:1305.3314v1
fatcat:dsud4ukekrffbhwdkzlwug5fei
*approximate**distance**oracle*is a succinct data structure that provides fast answers to*distance*queries between any two nodes. ... In this paper we consider*approximate**distance**oracles*for general undirected graphs with non-negative edge weights with constant query time. ... To overcome these drawbacks, much of the work on*distance**oracles*considers*approximated**distances*. ...##
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Approximate Distance Oracles with Improved Query Time
[chapter]

2014
*
Encyclopedia of Algorithms
*

Given an undirected graph G with m edges, n vertices, and non-negative edge weights, and given an integer k ≥ 2, we show that a (2k − 1)-

doi:10.1007/978-3-642-27848-8_568-1
fatcat:p5xmycz6dbemjhgp5du2altgeu
*approximate**distance**oracle*for G of size O(kn 1+1/k ) and with ... It is therefore natural to consider*approximate**distance**oracles*where some error in the reported*distances*is allowed. ... Since its query time is independent of the size of the graph (when k is), we refer to it as an*approximate**distance**oracle*. ...##
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Efficient Dynamic Approximate Distance Oracles for Vertex-Labeled Planar Graphs
[article]

2017
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arXiv
*
pre-print

A Vertex-Labeled

arXiv:1707.02414v2
fatcat:zw3jpwi6nvdkbi5ehqrecs2hxy
*Approximate**Distance**Oracle*is a data structure that, given a vertex v and a label λ, returns a (1+ε)-*approximation*of the*distance*from v to the closest vertex with label λ in G. ... In this paper we present three different dynamic*approximate*vertex-labeled*distance**oracles*for planar graphs, all with polylogarithmic query and update times, and nearly linear space requirements. ... We focus on*approximate*vertex-labeled*distance**oracles*for fixed parameter ε ≥ 0. When queried, such*oracle*returns at least the true*distance*, but not more than (1 + ε) times the true*distance*. ...##
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Space-Efficient Path-Reporting Approximate Distance Oracles
[article]

2014
*
arXiv
*
pre-print

For

arXiv:1410.0768v1
fatcat:betu3eo5pray7nrcdrt2454wei
*distance**oracles*, we show how to break the n n space bound of Thorup and Zwick if*approximate*paths rather than*distances*need to be reported. ... We consider*approximate*path-reporting*distance**oracles*,*distance*labeling and labeled routing with extremely low space requirement, for general undirected graphs. ... Conclusions We gave space-efficient*approximate**distance**oracles*,*distance*labeling, and labeled routing for undirected graphs. ...##
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Approximate Distance Oracles with Improved Query Time
[chapter]

2016
*
Encyclopedia of Algorithms
*

Given an undirected graph G with m edges, n vertices, and non-negative edge weights, and given an integer k ≥ 2, we show that a (2k − 1)-

doi:10.1007/978-1-4939-2864-4_568
fatcat:adaclkt7trefbokrjcxaccz3g4
*approximate**distance**oracle*for G of size O(kn 1+1/k ) and with ... It is therefore natural to consider*approximate**distance**oracles*where some error in the reported*distances*is allowed. ... Since its query time is independent of the size of the graph (when k is), we refer to it as an*approximate**distance**oracle*. ...##
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Approximate Distance Oracles with Improved Query Time
[chapter]

2013
*
Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms
*

Given an undirected graph G with m edges, n vertices, and non-negative edge weights, and given an integer k ≥ 2, we show that a (2k − 1)-

doi:10.1137/1.9781611973105.39
dblp:conf/soda/Wulff-Nilsen13
fatcat:cmzpmxyeivcjrnsg3cel4wpak4
*approximate**distance**oracle*for G of size O(kn 1+1/k ) and with ... It is therefore natural to consider*approximate**distance**oracles*where some error in the reported*distances*is allowed. ... Since its query time is independent of the size of the graph (when k is), we refer to it as an*approximate**distance**oracle*. ...##
###
Approximate Distance Oracles with Improved Preprocessing Time
[article]

2011
*
arXiv
*
pre-print

Given an undirected graph $G$ with $m$ edges, $n$ vertices, and non-negative edge weights, and given an integer $k\geq 1$, we show that for some universal constant $c$, a $(2k-1)$-

arXiv:1109.4156v1
fatcat:idmtsb5yurd5bnjb3jszeh4f3y
*approximate**distance*... We also give an*oracle*which is faster for smaller $k$. ... A (2k − 1)-*Approximate**Distance**Oracle*In this section, we present a (2k − 1)-*approximate**distance**oracle*with subquadratic preprocessing time for k ≥ 6. ...##
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Approximate Distance Oracles for Planar Graphs with Subpolynomial Error Dependency
[article]

2022
*
arXiv
*
pre-print

Thorup [FOCS'01, JACM'04] and Klein [SODA'01] independently showed that there exists a (1+ϵ)-

arXiv:2207.05659v1
fatcat:2vie7v36arfexdjmzm5aeqvn2y
*approximate**distance**oracle*for planar graphs with O(n (log n)ϵ^-1) space and O(ϵ^-1) query time. ... While the dependency on n is nearly linear, the space-query product of their*oracles*depend quadratically on 1/ϵ. ... All*approximate**distance**oracles*, including ours, use balanced shortest path separators. ...
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