research-article

Fully dynamic approximate distance oracles for planar graphs via forbidden-set distance labels

Authors:

Cyril GavoilleAuthors Info & Claims

STOC '12: Proceedings of the forty-fourth annual ACM symposium on Theory of computing

Pages 1199 - 1218

https://doi.org/10.1145/2213977.2214084

Published: 19 May 2012 Publication History

Abstract

This paper considers fully dynamic (1+ε) distance oracles and (1+ε) forbidden-set labeling schemes for planar graphs. For a given n-vertex planar graph G with edge weights drawn from [1,M] and parameter ε>0, our forbidden-set labeling scheme uses labels of length λ = O(ε^-1 log²n log(nM) • maxlogn). Given the labels of two vertices s and t and of a set F of faulty vertices/edges, our scheme approximates the distance between s and t in G \ F with stretch (1+ε), in O(|F|² λ) time.

We then present a general method to transform (1+ε) forbidden-set labeling schemas into a fully dynamic (1+ε) distance oracle. Our fully dynamic (1+ε) distance oracle is of size O(n log{n} • maxlogn) and has ~O(n^1/2) query and update time, both the query and the update time are worst case. This improves on the best previously known (1+ε) dynamic distance oracle for planar graphs, which has worst case query time ~O(n^2/3) and amortized update time of ~O(n^2/3).

Our (1+ε) forbidden-set labeling scheme can also be extended into a forbidden-set labeled routing scheme with stretch (1+ε).

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Cited By

Parter MPetruschka APettie SMohar BShinkar IO'Donnell R(2024)Connectivity Labeling and Routing with Multiple Vertex FailuresProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649729(823-834)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649729
Mao XMohar BShinkar IO'Donnell R(2024)Fully Dynamic All-Pairs Shortest Paths: Likely Optimal Worst-Case Update TimeProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649695(1141-1152)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649695
Izumi TEmek YWadayama TMasuzawa TOshman RNolin AHalldorsson MBalliu A(2023)Deterministic Fault-Tolerant Connectivity Labeling SchemeProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594584(190-199)Online publication date: 19-Jun-2023
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Index Terms

Fully dynamic approximate distance oracles for planar graphs via forbidden-set distance labels
1. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Conferences

STOC '12: Proceedings of the forty-fourth annual ACM symposium on Theory of computing

May 2012

1310 pages

ISBN:9781450312455

DOI:10.1145/2213977

General Chair:
Howard Karloff
AT&T Labs--Research
,
Program Chair:
Toniann Pitassi
University of Toronto

Copyright © 2012 ACM.

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Published: 19 May 2012

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May 19 - 22, 2012

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Cited By

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https://dl.acm.org/doi/10.1145/3618260.3649729
Mao XMohar BShinkar IO'Donnell R(2024)Fully Dynamic All-Pairs Shortest Paths: Likely Optimal Worst-Case Update TimeProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649695(1141-1152)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649695
Izumi TEmek YWadayama TMasuzawa TOshman RNolin AHalldorsson MBalliu A(2023)Deterministic Fault-Tolerant Connectivity Labeling SchemeProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594584(190-199)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594584
Van Den Brand JKarczmarz A(2023)Deterministic Fully Dynamic SSSP and More2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00142(2312-2321)Online publication date: 6-Nov-2023
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Charalampopoulos PMozes STebeka B(2022)Exact Distance Oracles for Planar Graphs with Failing VerticesACM Transactions on Algorithms10.1145/351154118:2(1-23)Online publication date: 30-Mar-2022
https://dl.acm.org/doi/10.1145/3511541
Raikwar HKarmakar S(2022)Fully Dynamic Algorithm for Steiner Tree using Dynamic Distance OracleProceedings of the 23rd International Conference on Distributed Computing and Networking10.1145/3491003.3491304(246-247)Online publication date: 4-Jan-2022
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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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Bar-Natan ACharalampopoulos PGawrychowski PMozes SWeimann O(2022)Fault-tolerant distance labeling for planar graphsTheoretical Computer Science10.1016/j.tcs.2022.03.020918:C(48-59)Online publication date: 29-May-2022
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Italiano GKarczmarz AParotsidis NMarx D(2021)Planar reachability under single vertex or edge failuresProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458227(2739-2758)Online publication date: 10-Jan-2021
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