research-article

A lower bound for the distributed Lovász local lemma

Authors:

Sebastian Brandt,

Barbara Keller,

Tuomo Lempiäinen,

Jara UittoAuthors Info & Claims

STOC '16: Proceedings of the forty-eighth annual ACM symposium on Theory of Computing

Pages 479 - 488

https://doi.org/10.1145/2897518.2897570

Published: 19 June 2016 Publication History

Abstract

We show that any randomised Monte Carlo distributed algorithm for the Lovász local lemma requires Omega(log log n) communication rounds, assuming that it finds a correct assignment with high probability. Our result holds even in the special case of d = O(1), where d is the maximum degree of the dependency graph. By prior work, there are distributed algorithms for the Lovász local lemma with a running time of O(log n) rounds in bounded-degree graphs, and the best lower bound before our work was Omega(log* n) rounds [Chung et al. 2014].

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http://www.cs.helsinki.fi/local-survey/. Introduction Distributed Lovász Local Lemma Main Result and Key Techniques Prior Work on LLL Prior Work on Other Lower Bounds Preliminaries Colourings Model of Computation Local Neighbourhoods Distributed Sinkless Orientation and Sinkless Colouring Distributed Lovász Local Lemma From LLL to Sinkless Orientation The Mutual Speedup Lemma From Sinkless Colouring to Sinkless Orientation From Sinkless Orientation Back to Sinkless Colouring The Speedup Lemma Lower Bounds Conclusions Acknowledgements References

Cited By

Balliu ABrandt SKuhn FNowicki KOlivetti DRotenberg ESuomela JKuznetsov PGelles ROlivetti D(2024)Brief Announcement: Local Advice and Local DecompressionProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662805(117-120)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662805
Balliu ABoudier TBrandt SOlivetti DKuznetsov PGelles ROlivetti D(2024)Tight Lower Bounds in the Supported LOCAL ModelProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662798(95-105)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662798
Coiteux-Roy Xd'Amore FGajjala RKuhn FLe Gall FLievonen HModanese ARenou MSchmid GSuomela JMohar BShinkar IO'Donnell R(2024)No Distributed Quantum Advantage for Approximate Graph ColoringProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649679(1901-1910)Online publication date: 10-Jun-2024
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Index Terms

A lower bound for the distributed Lovász local lemma
1. Mathematics of computing
  1. Probability and statistics
2. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Conferences

STOC '16: Proceedings of the forty-eighth annual ACM symposium on Theory of Computing

June 2016

1141 pages

ISBN:9781450341325

DOI:10.1145/2897518

General Chair:
Daniel Wichs
Northeastern, USA
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Program Chair:
Yishay Mansour
Tel Aviv

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Published: 19 June 2016

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Cited By

Balliu ABrandt SKuhn FNowicki KOlivetti DRotenberg ESuomela JKuznetsov PGelles ROlivetti D(2024)Brief Announcement: Local Advice and Local DecompressionProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662805(117-120)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662805
Balliu ABoudier TBrandt SOlivetti DKuznetsov PGelles ROlivetti D(2024)Tight Lower Bounds in the Supported LOCAL ModelProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662798(95-105)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662798
Coiteux-Roy Xd'Amore FGajjala RKuhn FLe Gall FLievonen HModanese ARenou MSchmid GSuomela JMohar BShinkar IO'Donnell R(2024)No Distributed Quantum Advantage for Approximate Graph ColoringProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649679(1901-1910)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649679
Czumaj ADavies-Peck PParter M(2024)Component stability in low-space massively parallel computationDistributed Computing10.1007/s00446-024-00461-937:1(35-64)Online publication date: 8-Feb-2024
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Lievonen HPicavet TSuomela J(2024)Distributed Binary Labeling Problems in High-Degree GraphsStructural Information and Communication Complexity10.1007/978-3-031-60603-8_22(402-419)Online publication date: 27-May-2024
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Maus Y(2023)Distributed Graph Coloring Made EasyACM Transactions on Parallel Computing10.1145/360589610:4(1-21)Online publication date: 17-Aug-2023
https://dl.acm.org/doi/10.1145/3605896
Chang YStudený JSuomela J(2023)Distributed graph problems through an automata-theoretic lensTheoretical Computer Science10.1016/j.tcs.2023.113710951:COnline publication date: 24-Mar-2023
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Balliu AGhaffari MKuhn FOlivetti D(2023)Node and edge averaged complexities of local graph problemsDistributed Computing10.1007/s00446-023-00453-136:4(451-473)Online publication date: 5-Jul-2023
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Adamson DHalldórsson MNolin A(2023)Distributed Coloring of HypergraphsStructural Information and Communication Complexity10.1007/978-3-031-32733-9_5(89-111)Online publication date: 25-May-2023
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Balliu ABrandt SKuhn FOlivetti DLeonardi SGupta A(2022)Distributed ∆-coloring plays hide-and-seekProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3520027(464-477)Online publication date: 9-Jun-2022
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