research-article

Approximate distance oracles for geometric spanners

Authors:

Joachim Gudmundsson,

Christos Levcopoulos,

Giri Narasimhan,

Michiel SmidAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 4, Issue 1

Article No.: 10, Pages 1 - 34

https://doi.org/10.1145/1328911.1328921

Published: 28 March 2008 Publication History

Abstract

Given an arbitrary real constant ε > 0, and a geometric graph G in d-dimensional 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 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 show that approximate shortest-path queries between vertices in a planar polygonal domain with “rounded” obstacles can be answered in constant time. Other applications include query versions of closest-pair problems, and the efficient computation of the approximate dilations of geometric graphs. Finally, we show how to extend the main result to answer (1 + ε)-approximate shortest-path-length queries in constant time for geometric spanner graphs with m = ω(n) edges. The resulting data structure can be constructed in O(m + n log n) time using O(n log n) space.

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Bhore SFiltser AKhodabandeh HTóth C(2024)Online Spanners in Metric SpacesSIAM Journal on Discrete Mathematics10.1137/22M153457238:1(1030-1056)Online publication date: 12-Mar-2024
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Index Terms

Approximate distance oracles for geometric spanners
1. Theory of computation
  1. Randomness, geometry and discrete structures

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cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 4, Issue 1

March 2008

343 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/1328911

Issue’s Table of Contents

Copyright © 2008 ACM.

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Publication History

Published: 28 March 2008

Accepted: 01 August 2007

Revised: 01 May 2006

Received: 01 April 2005

Published in TALG Volume 4, Issue 1

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Cited By

Cho KShin JOh EWooldridge MDy JNatarajan S(2024)Approximate distance oracle for fault-tolerant geometric spannersProceedings of the Thirty-Eighth AAAI Conference on Artificial Intelligence and Thirty-Sixth Conference on Innovative Applications of Artificial Intelligence and Fourteenth Symposium on Educational Advances in Artificial Intelligence10.1609/aaai.v38i18.29987(20087-20095)Online publication date: 20-Feb-2024
https://dl.acm.org/doi/10.1609/aaai.v38i18.29987
Bhore STóth C(2024)Online Euclidean SpannersACM Transactions on Algorithms10.1145/368179021:1(1-22)Online publication date: 4-Nov-2024
https://dl.acm.org/doi/10.1145/3681790
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https://doi.org/10.1137/22M1534572
Bhore STóth C(2022)Euclidean Steiner SpannersSIAM Journal on Discrete Mathematics10.1137/22M150270736:3(2411-2444)Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1137/22M1502707
Le HSolomon S(2022)Truly Optimal Euclidean SpannersSIAM Journal on Computing10.1137/20M1317906(FOCS19-135-FOCS19-199)Online publication date: 31-Mar-2022
https://doi.org/10.1137/20M1317906
Le HWulff-Nilsen C(2022)Optimal Approximate Distance Oracle for Planar Graphs2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS52979.2021.00044(363-374)Online publication date: Feb-2022
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An SOh E(2022)Reachability Problems for Transmission GraphsAlgorithmica10.1007/s00453-022-00985-184:10(2820-2841)Online publication date: 1-Oct-2022
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An SOh E(2021)Reachability Problems for Transmission GraphsAlgorithms and Data Structures10.1007/978-3-030-83508-8_6(71-84)Online publication date: 9-Aug-2021
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Le HSolomon S(2019)Truly Optimal Euclidean Spanners2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS.2019.00069(1078-1100)Online publication date: Nov-2019
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Gudmundsson JNarasimhan GSmid M(2016)Applications of Geometric Spanner NetworksEncyclopedia of Algorithms10.1007/978-1-4939-2864-4_15(86-90)Online publication date: 22-Apr-2016
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