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Efficient and Simple Algorithms for Fault-Tolerant Spanners

Authors:

Michael Dinitz,

Caleb RobelleAuthors Info & Claims

PODC '20: Proceedings of the 39th Symposium on Principles of Distributed Computing

Pages 493 - 500

https://doi.org/10.1145/3382734.3405735

Published: 31 July 2020 Publication History

Abstract

It was recently shown that a version of the greedy algorithm gives a construction of fault-tolerant spanners that is size-optimal, at least for vertex faults. However, the algorithm to construct this spanner is not polynomial-time, and the best-known polynomial time algorithm is significantly suboptimal. Designing a polynomial-time algorithm to construct (near-)optimal fault-tolerant spanners was given as an explicit open problem in the two most recent papers on fault-tolerant spanners ([Bodwin, Dinitz, Parter, Vassilevka Williams SODA '18] and [Bodwin, Patel PODC '19]). We give a surprisingly simple algorithm which runs in polynomial time and constructs fault-tolerant spanners that are extremely close to optimal (off by only a linear factor in the stretch) by modifying the greedy algorithm to run in polynomial time. To complement this result, we also give simple distributed constructions in both the LOCAL and CONGEST models.

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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
C. S. KParter M(2024)Deterministic Replacement Path CoveringACM Transactions on Algorithms10.1145/367376020:4(1-35)Online publication date: 5-Aug-2024
https://dl.acm.org/doi/10.1145/3673760
Manoharan VRamachandran V(2024)Computing Replacement Paths in the CONGEST ModelStructural Information and Communication Complexity10.1007/978-3-031-60603-8_23(420-437)Online publication date: 23-May-2024
https://doi.org/10.1007/978-3-031-60603-8_23
Show More Cited By

Index Terms

Efficient and Simple Algorithms for Fault-Tolerant Spanners
1. Theory of computation
  1. Design and analysis of algorithms
    1. Distributed algorithms
    2. Graph algorithms analysis
      1. Sparsification and spanners

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cover image ACM Conferences

PODC '20: Proceedings of the 39th Symposium on Principles of Distributed Computing

July 2020

539 pages

ISBN:9781450375825

DOI:10.1145/3382734

General Chair:
Yuval Emek
Technion, Israel
,
Program Chair:
Christian Cachin
University of Bern, Switzerland

Copyright © 2020 ACM.

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Publication History

Published: 31 July 2020

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National Science Foundation

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PODC '20

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PODC '20: ACM Symposium on Principles of Distributed Computing

August 3 - 7, 2020

Virtual Event, Italy

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Overall Acceptance Rate 740 of 2,477 submissions, 30%

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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
C. S. KParter M(2024)Deterministic Replacement Path CoveringACM Transactions on Algorithms10.1145/367376020:4(1-35)Online publication date: 5-Aug-2024
https://dl.acm.org/doi/10.1145/3673760
Manoharan VRamachandran V(2024)Computing Replacement Paths in the CONGEST ModelStructural Information and Communication Complexity10.1007/978-3-031-60603-8_23(420-437)Online publication date: 23-May-2024
https://doi.org/10.1007/978-3-031-60603-8_23
Dinitz MKoranteng AKortsarz GNutov Z(2023)Improved Approximations for Relative Survivable Network DesignApproximation and Online Algorithms 10.1007/978-3-031-49815-2_14(190-204)Online publication date: 7-Sep-2023
https://dl.acm.org/doi/10.1007/978-3-031-49815-2_14
Parter MLeonardi SGupta A(2022)Nearly optimal vertex fault-tolerant spanners in optimal time: sequential, distributed, and parallelProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3520047(1080-1092)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519935.3520047
Filtser ALe HLeonardi SGupta A(2022)Locality-sensitive orderings and applications to reliable spannersProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3520042(1066-1079)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519935.3520042
Bodwin GDinitz MRobelle CMarx D(2021)Optimal vertex fault-tolerant spanners in polynomial timeProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458238(2924-2938)Online publication date: 10-Jan-2021
https://dl.acm.org/doi/10.5555/3458064.3458238
Karthik CParter MMarx D(2021)Deterministic replacement path coveringProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458108(704-723)Online publication date: 10-Jan-2021
https://dl.acm.org/doi/10.5555/3458064.3458108

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