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Distributed Arboricity-Dependent Graph Coloring via All-to-All Communication

Authors Mohsen Ghaffari, Ali Sayyadi

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Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Mathematics of computing → Graph algorithms
Keywords
  • Distributed Computing
  • Message Passing Algorithms
  • Graph Coloring
  • Arboricity
  • Congested Clique Model
  • Randomized Algorithms

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Abstract

We present a constant-time randomized distributed algorithms in the congested clique model that computes an O(alpha)-vertex-coloring, with high probability. Here, alpha denotes the arboricity of the graph, which is, roughly speaking, the edge-density of the densest subgraph. Congested clique is a well-studied model of synchronous message passing for distributed computing with all-to-all communication: per round each node can send one O(log n)-bit message algorithm to each other node. Our O(1)-round algorithm settles the randomized round complexity of the O(alpha)-coloring problem. We also explain that a similar method can provide a constant-time randomized algorithm for decomposing the graph into O(alpha) edge-disjoint forests, so long as alpha <= n^{1-o(1)}.

Cite As Get BibTex

Mohsen Ghaffari and Ali Sayyadi. Distributed Arboricity-Dependent Graph Coloring via All-to-All Communication. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 142:1-142:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ICALP.2019.142

Author Details

Mohsen Ghaffari
  • ETH Zurich, Switzerland
Ali Sayyadi
  • Sharif University of Technology, Iran

Funding

The first author acknowledges the support of the Swiss National Foundation, under project number 200021_184735. The second author is grateful for the support of the Student Summer Research Fellowship (SSRF) program at the Computer Science department of ETH Zurich; this project was initiated during an undergraduate internship in the summer of 2018.

References

  1. Leonid Barenboim and Michael Elkin. Sublogarithmic distributed MIS algorithm for sparse graphs using Nash-Williams decomposition. Distributed Computing, 22(5-6):363-379, 2010. Google Scholar
  2. Leonid Barenboim and Michael Elkin. Deterministic distributed vertex coloring in polylogarithmic time. Journal of the ACM (JACM), 58(5):23, 2011. Google Scholar
  3. Leonid Barenboim and Michael Elkin. Distributed Graph Coloring: Fundamentals and Recent Developments. Synthesis Lectures on Distributed Computing Theory, 4(1):1-171, 2013. Google Scholar
  4. Leonid Barenboim, Michael Elkin, and Uri Goldenberg. Locally-Iterative Distributed (Δ+ 1):-Coloring below Szegedy-Vishwanathan Barrier, and Applications to Self-Stabilization and to Restricted-Bandwidth Models. In Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing, pages 437-446. ACM, 2018. Google Scholar
  5. Leonid Barenboim and Victor Khazanov. Distributed Symmetry-Breaking Algorithms for Congested Cliques. In International Computer Science Symposium in Russia, pages 41-52. Springer, 2018. Google Scholar
  6. Yi-Jun Chang, Manuela Fischer, Mohsen Ghaffari, Jara Uitto, and Yufan Zheng. The Complexity of (Δ+1) Coloring in Congested Clique, Massively Parallel Computation, and Centralized Local Computation. Manuscript, 2019. Google Scholar
  7. Yi-Jun Chang, Wenzheng Li, and Seth Pettie. An Optimal Distributed (Δ+1)-coloring Algorithm? In Proc. of the Symp. on Theory of Comp. (STOC), pages 445-456, 2018. Google Scholar
  8. Mohsen Ghaffari. Distributed MIS via all-to-all communication. In Proceedings of the ACM Symposium on Principles of Distributed Computing, pages 141-149. ACM, 2017. Google Scholar
  9. Mohsen Ghaffari. Distributed Maximal Independent Set using Small Messages. In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 805-820. SIAM, 2019. Google Scholar
  10. Mohsen Ghaffari and Christiana Lymouri. Simple and Near-Optimal Distributed Coloring for Sparse Graphs. In 31st International Symposium on Distributed Computing (DISC 2017). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2017. Google Scholar
  11. Mohsen Ghaffari and Merav Parter. MST in log-star rounds of congested clique. In Proc. of the Symp. on Princ. of Dist. Comp. (PODC), pages 19-28, 2016. Google Scholar
  12. James W. Hegeman and Sriram V. Pemmaraju. Lessons from the Congested Clique Applied to MapReduce. Theor. Comput. Sci., 608(P3):268-281, December 2015. Google Scholar
  13. Öjvind Johansson. Simple distributed Δ+ 1-coloring of graphs. Information Processing Letters, 70(5):229-232, 1999. Google Scholar
  14. Tomasz Jurdziński and Krzysztof Nowicki. MST in O (1) rounds of congested clique. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 2620-2632. SIAM, 2018. Google Scholar
  15. Christoph Lenzen. Optimal deterministic routing and sorting on the congested clique. In Proceedings of the 2013 ACM symposium on Principles of distributed computing, pages 42-50. ACM, 2013. Google Scholar
  16. Christoph Lenzen and Roger Wattenhofer. Brief announcement: Exponential speed-up of local algorithms using non-local communication. In Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing, pages 295-296. ACM, 2010. Google Scholar
  17. Nathan Linial. Locality in distributed graph algorithms. SIAM Journal on Computing (SICOMP), 21(1):193-201, 1992. Google Scholar
  18. Zvi Lotker, Boaz Patt-Shamir, Elan Pavlov, and David Peleg. Minimum-weight spanning tree construction in O (log log n) communication rounds. SIAM Journal on Computing, 35(1):120-131, 2005. Google Scholar
  19. C St JA Nash-Williams. Decomposition of finite graphs into forests. Journal of the London Mathematical Society, 1(1):12-12, 1964. Google Scholar
  20. Alessandro Panconesi and Aravind Srinivasan. Improved distributed algorithms for coloring and network decomposition problems. In Proc. of the Symp. on Theory of Comp. (STOC), pages 581-592. ACM, 1992. Google Scholar
  21. Merav Parter. (Δ+1) coloring in the congested clique model. In Proceedings of the International Colloquium on Automata, Languages and Programming (ICALP), 2018. Google Scholar
  22. Merav Parter and Hsin-Hao Su. (Δ+1) coloring in O(log^∗ Δ) congested-clique rounds. In Proceedings of the International Symposium on Distributed Computing (DISC), 2018. Google Scholar
  23. David Peleg. Distributed Computing: A Locality-sensitive Approach. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2000. Google Scholar
  24. Sriram V Pemmaraju. Equitable coloring extends Chernoff-Hoeffding bounds. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques, pages 285-296. Springer, 2001. Google Scholar
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