A Lower Bound on Probabilistic Algorithms for Distributive Ring Coloring
Abstract
Suppose that n processors are arranged in a ring and can communicate only with their immediate neighbors. It is shown that any probabilistic algorithm for 3 coloring the ring must take at least $\frac{1}{2}\log^* n - 2$ rounds, otherwise the probability that all processors are colored legally is less than $\frac{1}{2}$. A similar time bound holds for selecting a maximal independent set. The bound is tight (up to a constant factor) in light of the deterministic algorithms of Cole and Vishkin [Inform, and Control, 70 (1986), pp. 32–53] and extends the lower bound for deterministic algorithms of Linial [Proc. 28th IEEE Foundations of Computer Science Symposium, 1987, pp. 331–335].
MSC codes
Keywords
Get full access to this article
View all available purchase options and get full access to this article.
References
BNN.
Amotz Bar-Noy, Joseph Naor, Moni Naor, One-bit algorithms, Distrib. Comput., 4 (1990), 3–8
CV.
Richard Cole, Uzi Vishkin, Deterministic coin tossing with applications to optimal parallel list ranking, Inform. and Control, 70 (1986), 32–53
GPS.
A. Goldberg, S. Plotkin, G. Shannon, Efficient parallel algorithms for (Δ+1)-coloring and maximal independent set problems, Proc. 19th ACM Symp. on Theory of Computing, 1987, 315–324
L.
N. Linial, Distributive graphs algorithms—global solutions from local data, Proc. 28th IEEE Foundations of Computer Science Symposium, 1987, 331–335
Information & Authors
Information
Published In
Copyright
Copyright © 1991 Society for Industrial and Applied Mathematics.
History
Submitted: 20 June 1990
Accepted: 4 September 1990
Published online: 8 August 2006
MSC codes
Keywords
Authors
Metrics & Citations
Metrics
Citations
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited By
- Distributed half-integral matching and beyondTheoretical Computer Science, Vol. 982 | 1 Jan 2024
- Symmetrization for finitely dependent colouringElectronic Communications in Probability, Vol. 29, No. none | 1 Jan 2024
- Distributed Graph Coloring Made EasyACM Transactions on Parallel Computing, Vol. 10, No. 4 | 14 December 2023
- Node and edge averaged complexities of local graph problemsDistributed Computing, Vol. 36, No. 4 | 5 July 2023
- Locally checkable problems in rooted treesDistributed Computing, Vol. 36, No. 3 | 22 August 2022
- Brief Announcement: List Defective Colorings: Distributed Algorithms and ApplicationsProceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures | 17 June 2023
- Distributed Half-Integral Matching and BeyondStructural Information and Communication Complexity | 25 May 2023
- Linial for listsDistributed Computing, Vol. 35, No. 6 | 17 May 2022
- Node and Edge Averaged Complexities of Local Graph ProblemsProceedings of the 2022 ACM Symposium on Principles of Distributed Computing | 21 July 2022
- The Landscape of Distributed Complexities on Trees and BeyondProceedings of the 2022 ACM Symposium on Principles of Distributed Computing | 21 July 2022
- Average Awake Complexity of MIS and MatchingProceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures | 11 July 2022
- Near-optimal distributed degree+1 coloringProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing | 10 June 2022
- Distributed ∆-coloring plays hide-and-seekProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing | 10 June 2022
- Distributed Lower Bounds for Ruling SetsSIAM Journal on Computing, Vol. 51, No. 1 | 8 February 2022
- Randomized Local Network Computing: Derandomization Beyond Locally Checkable LabelingsACM Transactions on Parallel Computing, Vol. 8, No. 4 | 15 October 2021
- Lower Bounds for Maximal Matchings and Maximal Independent SetsJournal of the ACM, Vol. 68, No. 5 | 6 December 2021
- Improved Distributed Lower Bounds for MIS and Bounded (Out-)Degree Dominating Sets in TreesProceedings of the 2021 ACM Symposium on Principles of Distributed Computing | 23 July 2021
- Can We Break Symmetry with o(m) Communication?Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing | 23 July 2021
- Locally Checkable Problems in Rooted TreesProceedings of the 2021 ACM Symposium on Principles of Distributed Computing | 23 July 2021
- Efficient Load-Balancing through Distributed Token DroppingProceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures | 6 July 2021
- Distributed Graph Coloring Made EasyProceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures | 6 July 2021
- Fooling views: a new lower bound technique for distributed computations under congestionDistributed Computing, Vol. 33, No. 6 | 9 April 2020
- Distributed Lower Bounds for Ruling Sets2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS) | 1 Nov 2020
- Using Round Elimination to Understand LocalityACM SIGACT News, Vol. 51, No. 3 | 29 September 2020
- Brief Announcement: Round eliminator: a tool for automatic speedup simulationProceedings of the 39th Symposium on Principles of Distributed Computing | 31 July 2020
- How much does randomness help with locally checkable problems?Proceedings of the 39th Symposium on Principles of Distributed Computing | 31 July 2020
- Seeing Far vs. Seeing Wide: Volume Complexity of Local Graph ProblemsProceedings of the 39th Symposium on Principles of Distributed Computing | 31 July 2020
- Truly Tight-in-Δ Bounds for Bipartite Maximal Matching and VariantsProceedings of the 39th Symposium on Principles of Distributed Computing | 31 July 2020
- Finitely dependent processes are finitaryThe Annals of Probability, Vol. 48, No. 4 | 1 Jul 2020
- How long it takes for an ordinary node with an ordinary id to output?Theoretical Computer Science, Vol. 811 | 1 Apr 2020
- Distributed Edge Coloring and a Special Case of the Constructive Lovász Local LemmaACM Transactions on Algorithms, Vol. 16, No. 1 | 15 November 2019
- Distributed $(\Delta+1)$-Coloring via Ultrafast Graph ShatteringSIAM Journal on Computing, Vol. 49, No. 3 | 19 May 2020
- Mallows permutations and finite dependenceThe Annals of Probability, Vol. 48, No. 1 | 1 Jan 2020
- Lower Bounds for Maximal Matchings and Maximal Independent Sets2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS) | 1 Nov 2019
- Conditional Hardness Results for Massively Parallel Computation from Distributed Lower Bounds2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS) | 1 Nov 2019
- Hardness of Minimal Symmetry Breaking in Distributed ComputingProceedings of the 2019 ACM Symposium on Principles of Distributed Computing | 16 July 2019
- The Distributed Complexity of Locally Checkable Problems on Paths is DecidableProceedings of the 2019 ACM Symposium on Principles of Distributed Computing | 16 July 2019
- An Exponential Separation between Randomized and Deterministic Complexity in the LOCAL ModelSIAM Journal on Computing, Vol. 48, No. 1 | 30 January 2019
- A Time Hierarchy Theorem for the LOCAL ModelSIAM Journal on Computing, Vol. 48, No. 1 | 3 January 2019
- Locality of Not-so-Weak ColoringStructural Information and Communication Complexity | 13 July 2019
- Localisation-Resistant Random Words with Small AlphabetsCombinatorics on Words | 9 August 2019
- Distributed (Δ +1)-Coloring in Sublogarithmic RoundsJournal of the ACM, Vol. 65, No. 4 | 12 April 2018
- An optimal distributed (Δ+1)-coloring algorithm?Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing | 20 June 2018
- A Time Hierarchy Theorem for the LOCAL Model2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) | 1 Oct 2017
- Finitary coloringThe Annals of Probability, Vol. 45, No. 5 | 1 Sep 2017
- One-dependent coloring by finitary factorsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 53, No. 2 | 1 May 2017
- How Long It Takes for an Ordinary Node with an Ordinary ID to Output?Structural Information and Communication Complexity | 30 December 2017
- An Exponential Separation between Randomized and Deterministic Complexity in the LOCAL Model2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) | 1 Oct 2016
- Local Conflict Coloring2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) | 1 Oct 2016
- Brief AnnouncementProceedings of the 2016 ACM Symposium on Principles of Distributed Computing | 25 July 2016
- A lower bound for the distributed Lovász local lemmaProceedings of the forty-eighth annual ACM symposium on Theory of Computing | 19 June 2016
- Locality in Distributed Graph AlgorithmsEncyclopedia of Algorithms | 22 April 2016
- FINITELY DEPENDENT COLORINGForum of Mathematics, Pi, Vol. 4 | 3 November 2016
- Randomized Local Network ComputingProceedings of the 27th ACM symposium on Parallelism in Algorithms and Architectures | 13 June 2015
- Exact Bounds for Distributed Graph ColouringStructural Information and Communication Complexity | 20 November 2015
- Locality in Distributed Graph AlgorithmsEncyclopedia of Algorithms | 18 April 2015
- Randomized distributed decisionDistributed Computing, Vol. 27, No. 6 | 6 April 2014
- Towards a complexity theory for local distributed computingJournal of the ACM, Vol. 60, No. 5 | 28 October 2013
- Lower bounds for local approximationJournal of the ACM, Vol. 60, No. 5 | 28 October 2013
- Optimal deterministic routing and sorting on the congested cliqueProceedings of the 2013 ACM symposium on Principles of distributed computing | 22 July 2013
- Distributed minimum dominating set approximations in restricted families of graphsDistributed Computing, Vol. 26, No. 2 | 27 March 2013
- Survey of local algorithmsACM Computing Surveys, Vol. 45, No. 2 | 12 March 2013
- Distributed Graph ColoringSynthesis Lectures on Distributed Computing Theory | 26 March 2022
- Distributed algorithms for sensor networksPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 370, No. 1958 | 13 January 2012
- Randomized Distributed DecisionDistributed Computing | 1 Jan 2012
- Local Distributed Decision2011 IEEE 52nd Annual Symposium on Foundations of Computer Science | 1 Oct 2011
- Tight bounds for parallel randomized load balancingProceedings of the forty-third annual ACM symposium on Theory of computing | 6 June 2011
- MIS on treesProceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing | 6 June 2011
- Distributed computing with advice: information sensitivity of graph coloringDistributed Computing, Vol. 21, No. 6 | 9 January 2009
- What Can Be Observed Locally?Distributed Computing | 1 Jan 2009
- A Primal-Dual Bicriteria Distributed Algorithm for Capacitated Vertex CoverSIAM Journal on Computing, Vol. 38, No. 3 | 28 May 2008
- Leveraging Linial’s Locality LimitDistributed Computing | 1 Jan 2008
- A randomized distributed algorithm for the maximal independent set problem in growth-bounded graphsProceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing | 12 August 2007
- On the Distributed Complexity of Computing Maximal MatchingsSIAM Journal on Discrete Mathematics, Vol. 15, No. 1 | 1 August 2006
- A faster distributed algorithm for computing maximal matchings deterministicallyProceedings of the eighteenth annual ACM symposium on Principles of distributed computing | 1 May 1999
- What Can be Computed Locally?SIAM Journal on Computing, Vol. 24, No. 6 | 13 July 2006
- Local computations on static and dynamic graphsProceedings Third Israel Symposium on the Theory of Computing and Systems | 1 Jan 1995
- Local-Global Phenomena in GraphsCombinatorics, Probability and Computing, Vol. 2, No. 4 | 12 September 2008
View Options
- Access via your Institution
- Questions about how to access this content? Contact SIAM at [email protected].