research-article

Sublogarithmic distributed MIS algorithm for sparse graphs using nash-williams decomposition

Authors:

Leonid Barenboim,

Michael ElkinAuthors Info & Claims

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

Pages 25 - 34

https://doi.org/10.1145/1400751.1400757

Published: 18 August 2008 Publication History

Abstract

We study the distributed maximal independent set (henceforth, MIS) problem on sparse graphs. Currently, there are known algorithms with a sublogarithmic running time for this problem on oriented trees and graphs of bounded degrees. We devise the first sublogarithmic algorithm for computing MIS on graphs of bounded arboricity. This is a large family of graphs that includes graphs of bounded degree, planar graphs, graphs of bounded genus, graphs of bounded treewidth, graphs that exclude a fixed minor, and many other graphs. We also devise efficient algorithms for coloring graphs from these families. These results are achieved by the following technique that may be of independent interest. Our algorithm starts with computing a certain graph-theoretic structure, called Nash-Williams forests-decomposition. Then this structure is used to compute the MIS or coloring. Our results demonstrate that this methodology is very powerful. Finally, we show nearly-tight lower bounds on the running time of any distributed algorithm for computing a forests-decomposition.

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Cited By

Li RGao SQin LWang GYang WYu J(2020)Ordering heuristics for k-clique listingProceedings of the VLDB Endowment10.14778/3407790.340784313:12(2536-2548)Online publication date: 14-Sep-2020
https://dl.acm.org/doi/10.14778/3407790.3407843
Chechik SMukhtar DChan T(2019)Optimal distributed coloring algorithms for planar graphs in the LOCAL modelProceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3310435.3310484(787-804)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.5555/3310435.3310484
Barenboim LTzur YHansdah RKrishnaswamy DVaidya N(2019)Distributed symmetry-breaking with improved vertex-averaged complexityProceedings of the 20th International Conference on Distributed Computing and Networking10.1145/3288599.3288601(31-40)Online publication date: 4-Jan-2019
https://dl.acm.org/doi/10.1145/3288599.3288601
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Index Terms

Sublogarithmic distributed MIS algorithm for sparse graphs using nash-williams decomposition
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Network flows
2. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis
      1. Network flows
  2. Randomness, geometry and discrete structures

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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.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 18 August 2008

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PODC '08: ACM Symposium on Principles of Distributed Computing

August 18 - 21, 2008

Toronto, Canada

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

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Cited By

Li RGao SQin LWang GYang WYu J(2020)Ordering heuristics for k-clique listingProceedings of the VLDB Endowment10.14778/3407790.340784313:12(2536-2548)Online publication date: 14-Sep-2020
https://dl.acm.org/doi/10.14778/3407790.3407843
Chechik SMukhtar DChan T(2019)Optimal distributed coloring algorithms for planar graphs in the LOCAL modelProceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3310435.3310484(787-804)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.5555/3310435.3310484
Barenboim LTzur YHansdah RKrishnaswamy DVaidya N(2019)Distributed symmetry-breaking with improved vertex-averaged complexityProceedings of the 20th International Conference on Distributed Computing and Networking10.1145/3288599.3288601(31-40)Online publication date: 4-Jan-2019
https://dl.acm.org/doi/10.1145/3288599.3288601
Barenboim LTzur YScheideler CFineman J(2018)Brief AnnouncementProceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures10.1145/3210377.3210660(223-226)Online publication date: 11-Jul-2018
https://dl.acm.org/doi/10.1145/3210377.3210660
Fischer OGonen TKuhn FOshman RScheideler CFineman J(2018)Possibilities and Impossibilities for Distributed Subgraph DetectionProceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures10.1145/3210377.3210401(153-162)Online publication date: 11-Jul-2018
https://dl.acm.org/doi/10.1145/3210377.3210401
Barenboim LMaimon T(2018)Distributed Symmetry Breaking in Graphs with Bounded Diversity2018 IEEE International Parallel and Distributed Processing Symposium (IPDPS)10.1109/IPDPS.2018.00082(723-732)Online publication date: May-2018
https://doi.org/10.1109/IPDPS.2018.00082
Beauquier JBurman JDufoulon FKutten S(2018)Fast Beeping Protocols for Deterministic MIS and (Δ + 1)-Coloring in Sparse GraphsIEEE INFOCOM 2018 - IEEE Conference on Computer Communications10.1109/INFOCOM.2018.8486015(1754-1762)Online publication date: Apr-2018
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Barenboim LKhazanov V(2018)Distributed Symmetry-Breaking Algorithms for Congested CliquesComputer Science – Theory and Applications10.1007/978-3-319-90530-3_5(41-52)Online publication date: 25-Apr-2018
https://doi.org/10.1007/978-3-319-90530-3_5
Barenboim LElkin MMaimon TSchiller ESchwarzmann A(2017)Deterministic Distributed (Delta + o(Delta))-Edge-Coloring, and Vertex-Coloring of Graphs with Bounded DiversityProceedings of the ACM Symposium on Principles of Distributed Computing10.1145/3087801.3087812(175-184)Online publication date: 25-Jul-2017
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Nayyaroddeen SGambhir MKothapalli K(2017)A Study of Graph Decomposition Algorithms for Parallel Symmetry Breaking2017 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)10.1109/IPDPSW.2017.120(598-607)Online publication date: May-2017
https://doi.org/10.1109/IPDPSW.2017.120
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