research-article

Forbidden-Set Distance Labels for Graphs of Bounded Doubling Dimension

Authors:

Cyril Gavoille,

David PelegAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 12, Issue 2

Article No.: 22, Pages 1 - 17

https://doi.org/10.1145/2818694

Published: 12 February 2016 Publication History

Abstract

This article proposes a forbidden-set labeling scheme for the family of unweighted graphs with doubling dimension bounded by α. For an n-vertex graph G in this family, and for any desired precision parameter ϵ > 0, the labeling scheme stores an O(1 + ϵ^{− 1})^2αlog ²n-bit label at each vertex. Given the labels of two end-vertices s and t, and the labels of a set F of “forbidden” vertices and/or edges, our scheme can compute, in O(1 + ϵ^{− 1})^2α · |F|²log n time, a 1 + ϵ stretch approximation for the distance between s and t in the graph G∖F. The labeling scheme can be extended into a forbidden-set labeled routing scheme with stretch 1 + ϵ for graphs of bounded doubling dimension.

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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
Izumi TEmek YWadayama TMasuzawa T(2024)Deterministic fault-tolerant connectivity labeling schemeDistributed Computing10.1007/s00446-024-00472-6Online publication date: 4-Nov-2024
https://doi.org/10.1007/s00446-024-00472-6
Bodwin GParter M(2023)Restorable Shortest Path Tiebreaking for Edge-Faulty GraphsJournal of the ACM10.1145/360354270:5(1-24)Online publication date: 11-Oct-2023
https://dl.acm.org/doi/10.1145/3603542
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Index Terms

Forbidden-Set Distance Labels for Graphs of Bounded Doubling Dimension
1. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 12, Issue 2

February 2016

385 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/2846106

Editor:
Aravind Srinivasan
University of Maryland, USA

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Copyright © 2016 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 12 February 2016

Accepted: 01 June 2015

Revised: 01 June 2015

Received: 01 June 2014

Published in TALG Volume 12, Issue 2

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United States-Israel Binational Science Foundation
Israel Science Foundation
Israel Ministry of Science and Technology (infrastructures grant)

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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
Izumi TEmek YWadayama TMasuzawa T(2024)Deterministic fault-tolerant connectivity labeling schemeDistributed Computing10.1007/s00446-024-00472-6Online publication date: 4-Nov-2024
https://doi.org/10.1007/s00446-024-00472-6
Bodwin GParter M(2023)Restorable Shortest Path Tiebreaking for Edge-Faulty GraphsJournal of the ACM10.1145/360354270:5(1-24)Online publication date: 11-Oct-2023
https://dl.acm.org/doi/10.1145/3603542
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
Busch CChen DFiltser AHathcock DHershkowitz DRajaraman R(2023)One Tree to Rule Them All: Poly-Logarithmic Universal Steiner Tree2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00012(60-76)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00012
Bonamy MGavoille CPilipczuk M(2022)Shorter Labeling Schemes for Planar GraphsSIAM Journal on Discrete Mathematics10.1137/20M133046436:3(2082-2099)Online publication date: 31-Aug-2022
https://doi.org/10.1137/20M1330464
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
https://dl.acm.org/doi/10.1016/j.tcs.2022.03.020
Dory MParter MMiller ACensor-Hillel K(2021)Fault-Tolerant Labeling and Compact Routing SchemesProceedings of the 2021 ACM Symposium on Principles of Distributed Computing10.1145/3465084.3467929(445-455)Online publication date: 21-Jul-2021
https://dl.acm.org/doi/10.1145/3465084.3467929
Bar-Natan ACharalampopoulos PGawrychowski PMozes SWeimann O(2021)Fault-Tolerant Distance Labeling for Planar GraphsStructural Information and Communication Complexity10.1007/978-3-030-79527-6_18(315-333)Online publication date: 20-Jun-2021
https://doi.org/10.1007/978-3-030-79527-6_18
Bonamy MGavoille CPilipczuk MChawla S(2020)Shorter labeling schemes for planar graphsProceedings of the Thirty-First Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3381089.3381116(446-462)Online publication date: 5-Jan-2020
https://dl.acm.org/doi/10.5555/3381089.3381116
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