research-article

On the locality of distributed sparse spanner construction

Authors:

Cyril Gavoille,

Laurent ViennotAuthors Info & Claims

PODC '08: Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing

Pages 273 - 282

https://doi.org/10.1145/1400751.1400788

Published: 18 August 2008 Publication History

Abstract

The paper presents a deterministic distributed algorithm that, given k ≥ 1, constructs in k rounds a (2k-1,0)-spanner of O(k n^1+1/k) edges for every n-node unweighted graph. (If n is not available to the nodes, then our algorithm executes in 3k-2 rounds, and still returns a (2k-1,0)-spanner with O(k n^1+1/k) edges.) Previous distributed solutions achieving such optimal stretch-size trade-off either make use of randomization providing performance guarantees in expectation only, or perform in log^Ω(1)n rounds, and all require a priori knowledge of n. Based on this algorithm, we propose a second deterministic distributed algorithm that, for every ε > 0, constructs a (1+ε,2)-spanner of O(ε^-1 n^3/2) edges in O(ε^-1) rounds, without any prior knowledge on the graph.

Our algorithms are complemented with lower bounds, which hold even under the assumption that n is known to the nodes. It is shown that any (randomized) distributed algorithm requires k rounds in expectation to compute a (2k-1,0)-spanner of o(n^1+1/(k-1)) edges for k ∈ {2,3,5}. It is also shown that for every k>1, any (randomized) distributed algorithm that constructs a spanner with fewer than n^{1+1/k + ε} edges in at most n^ε expected rounds must stretch some distances by an additive factor of n^Ω(ε). In other words, while additive stretched spanners with O(n^1+1/k) edges may exist, e.g., for k=2,3, they cannot be computed distributively in a sub-polynomial number of rounds in expectation.

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Cited By

Ji HPemmaraju S(2024)Towards Singular Optimality in the Presence of Local Initial KnowledgeStructural Information and Communication Complexity10.1007/978-3-031-60603-8_17(300-317)Online publication date: 23-May-2024
https://doi.org/10.1007/978-3-031-60603-8_17
Bezdrighin MElkin MGhaffari MGrunau CHaeupler BIlchi SRozhoň VAgrawal KLee I(2022)Deterministic Distributed Sparse and Ultra-Sparse Spanners and Connectivity CertificatesProceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3490148.3538565(1-10)Online publication date: 11-Jul-2022
https://dl.acm.org/doi/10.1145/3490148.3538565
Robinson PMarx D(2021)Being fast means being chattyProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458190(2105-2120)Online publication date: 10-Jan-2021
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Index Terms

On the locality of distributed sparse spanner construction
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Networks
  1. Network architectures

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cover image ACM Conferences

PODC '08: Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing

August 2008

474 pages

ISBN:9781595939890

DOI:10.1145/1400751

General Chair:
Rida Bazzi
Arizona State University, USA
,
Program Chair:
Boaz Patt-Shamir
Tel Aviv University, Israel

Copyright © 2008 ACM.

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Published: 18 August 2008

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Cited By

Ji HPemmaraju S(2024)Towards Singular Optimality in the Presence of Local Initial KnowledgeStructural Information and Communication Complexity10.1007/978-3-031-60603-8_17(300-317)Online publication date: 23-May-2024
https://doi.org/10.1007/978-3-031-60603-8_17
Bezdrighin MElkin MGhaffari MGrunau CHaeupler BIlchi SRozhoň VAgrawal KLee I(2022)Deterministic Distributed Sparse and Ultra-Sparse Spanners and Connectivity CertificatesProceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3490148.3538565(1-10)Online publication date: 11-Jul-2022
https://dl.acm.org/doi/10.1145/3490148.3538565
Robinson PMarx D(2021)Being fast means being chattyProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458190(2105-2120)Online publication date: 10-Jan-2021
https://dl.acm.org/doi/10.5555/3458064.3458190
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
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Elkin MFiltser ANeiman OEmek YCachin C(2020)Distributed Construction of Light NetworksProceedings of the 39th Symposium on Principles of Distributed Computing10.1145/3382734.3405701(483-492)Online publication date: 31-Jul-2020
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Censor-Hillel KParter MSchwartzman G(2020)Derandomizing local distributed algorithms under bandwidth restrictionsDistributed Computing10.1007/s00446-020-00376-1Online publication date: 18-Apr-2020
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Barenboim LMaimon T(2020)Simple Distributed Spanners in Dense Congest NetworksSOFSEM 2020: Theory and Practice of Computer Science10.1007/978-3-030-38919-2_22(260-272)Online publication date: 17-Jan-2020
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Elkin MMatar SRobinson PEllen F(2019)Near-Additive Spanners In Low Polynomial Deterministic CONGEST TimeProceedings of the 2019 ACM Symposium on Principles of Distributed Computing10.1145/3293611.3331635(531-540)Online publication date: 16-Jul-2019
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Lenzen CPatt-Shamir BPeleg D(2019)Distributed distance computation and routing with small messagesDistributed Computing10.1007/s00446-018-0326-632:2(133-157)Online publication date: 1-Apr-2019
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Elkin MNeiman O(2018)Efficient Algorithms for Constructing Very Sparse Spanners and EmulatorsACM Transactions on Algorithms10.1145/327465115:1(1-29)Online publication date: 16-Nov-2018
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