research-article

Streaming and fully dynamic centralized algorithms for constructing and maintaining sparse spanners

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Michael ElkinAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 7, Issue 2

Article No.: 20, Pages 1 - 17

https://doi.org/10.1145/1921659.1921666

Published: 31 March 2011 Publication History

Abstract

We present a streaming algorithm for constructing sparse spanners and show that our algorithm significantly outperforms the state-of-the-art algorithm for this task (due to Feigenbaum et al.). Specifically, the processing time per edge of our algorithm is O(1), and it is drastically smaller than that of the algorithm of Feigenbaum et al., and all other efficiency parameters of our algorithm are no greater (and some of them are strictly smaller) than the respective parameters of the state-of-the-art algorithm.

We also devise a fully dynamic centralized algorithm maintaining sparse spanners. This algorithm has incremental update time of O(1), and a nontrivial decremental update time. To our knowledge, this is the first fully dynamic centralized algorithm for maintaining sparse spanners that provides nontrivial bounds on both incremental and decremental update time for a wide range of stretch parameter t.

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Cited By

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
https://doi.org/10.1137/22M1534572
Becker REmek YGhaffari MLenzen C(2024)Decentralized Low-Stretch Trees via Low Diameter Graph DecompositionsSIAM Journal on Computing10.1137/22M148903453:2(247-286)Online publication date: 13-Mar-2024
https://doi.org/10.1137/22M1489034
Jiang ZChen HJin H(2023)Auxo: A Scalable and Efficient Graph Stream Summarization StructureProceedings of the VLDB Endowment10.14778/3583140.358315416:6(1386-1398)Online publication date: 20-Apr-2023
https://dl.acm.org/doi/10.14778/3583140.3583154
Show More Cited By

Index Terms

Streaming and fully dynamic centralized algorithms for constructing and maintaining sparse spanners
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
2. Theory of computation
  1. Randomness, geometry and discrete structures

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cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 7, Issue 2

March 2011

284 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/1921659

Issue’s Table of Contents

Copyright © 2011 ACM.

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Association for Computing Machinery

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Publication History

Published: 31 March 2011

Accepted: 01 March 2009

Revised: 01 March 2009

Received: 01 July 2008

Published in TALG Volume 7, Issue 2

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Israel Academy of Sciences and Humanities

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Cited By

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
https://doi.org/10.1137/22M1534572
Becker REmek YGhaffari MLenzen C(2024)Decentralized Low-Stretch Trees via Low Diameter Graph DecompositionsSIAM Journal on Computing10.1137/22M148903453:2(247-286)Online publication date: 13-Mar-2024
https://doi.org/10.1137/22M1489034
Jiang ZChen HJin H(2023)Auxo: A Scalable and Efficient Graph Stream Summarization StructureProceedings of the VLDB Endowment10.14778/3583140.358315416:6(1386-1398)Online publication date: 20-Apr-2023
https://dl.acm.org/doi/10.14778/3583140.3583154
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
Elkin MTrehan CMilani AWoelfel P(2022)Brief Announcement: (1+ε)-Approximate Shortest Paths in Dynamic Streams.Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing10.1145/3519270.3538469(57-59)Online publication date: 20-Jul-2022
https://dl.acm.org/doi/10.1145/3519270.3538469
Brand JForster SNazari Y(2022)Fast Deterministic Fully Dynamic Distance Approximation2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS54457.2022.00099(1011-1022)Online publication date: Oct-2022
https://doi.org/10.1109/FOCS54457.2022.00099
Bergamaschi THenzinger MGutenberg MWilliams VWein NMarx D(2021)New techniques and fine-grained hardness for dynamic near-additive spannersProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458174(1836-1855)Online publication date: 10-Jan-2021
https://dl.acm.org/doi/10.5555/3458064.3458174
Dory MFischer OKhoury SLeitersdorf DMiller ACensor-Hillel K(2021)Constant-Round Spanners and Shortest Paths in Congested Clique and MPCProceedings of the 2021 ACM Symposium on Principles of Distributed Computing10.1145/3465084.3467928(223-233)Online publication date: 21-Jul-2021
https://dl.acm.org/doi/10.1145/3465084.3467928
Becker RForster SKarrenbauer ALenzen C(2021)Near-Optimal Approximate Shortest Paths and Transshipment in Distributed and Streaming ModelsSIAM Journal on Computing10.1137/19M128695550:3(815-856)Online publication date: 4-May-2021
https://doi.org/10.1137/19M1286955
Assadi SKol GSaxena RYu H(2020)Multi-Pass Graph Streaming Lower Bounds for Cycle Counting, MAX-CUT, Matching Size, and Other Problems2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS46700.2020.00041(354-364)Online publication date: Nov-2020
https://doi.org/10.1109/FOCS46700.2020.00041
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