Improved Network Decompositions Using Small Messages with Applications on MIS, Neighborhood Covers, and Beyond

Authors Mohsen Ghaffari, Julian Portmann

Thumbnail PDF


  • Filesize: 452 kB
  • 16 pages

Document Identifiers

Author Details

Mohsen Ghaffari
  • ETH Zurich, Switzerland
Julian Portmann
  • ETH Zürich, Switzerland

Cite AsGet BibTex

Mohsen Ghaffari and Julian Portmann. Improved Network Decompositions Using Small Messages with Applications on MIS, Neighborhood Covers, and Beyond. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Network decompositions, as introduced by Awerbuch, Luby, Goldberg, and Plotkin [FOCS'89], are one of the key algorithmic tools in distributed graph algorithms. We present an improved deterministic distributed algorithm for constructing network decompositions of power graphs using small messages, which improves upon the algorithm of Ghaffari and Kuhn [DISC'18]. In addition, we provide a randomized distributed network decomposition algorithm, based on our deterministic algorithm, with failure probability exponentially small in the input size that works with small messages as well. Compared to the previous algorithm of Elkin and Neiman [PODC'16], our algorithm achieves a better success probability at the expense of its round complexity, while giving a network decomposition of the same quality. As a consequence of the randomized algorithm for network decomposition, we get a faster randomized algorithm for computing a Maximal Independent Set, improving on a result of Ghaffari [SODA'19]. Other implications of our improved deterministic network decomposition algorithm are: a faster deterministic distributed algorithms for constructing spanners and approximations of distributed set cover, improving results of Ghaffari, and Kuhn [DISC'18] and Deurer, Kuhn, and Maus [PODC'19]; and faster a deterministic distributed algorithm for constructing neighborhood covers, resolving an open question of Elkin [SODA'04].

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Distributed Graph Algorithms
  • Network Decomposition
  • Maximal Independent Set
  • Neighborhood Cover


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Yehuda Afek and Moty Ricklin. Sparser: A paradigm for running distributed algorithms. Journal of Algorithms, 14(2):316-328, 1993. Google Scholar
  2. Noga Alon, László Babai, and Alon Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. Journal of algorithms, 7(4):567-583, 1986. Google Scholar
  3. Noga Alon, Ronitt Rubinfeld, Shai Vardi, and Ning Xie. Space-efficient local computation algorithms. In Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms, pages 1132-1139. Society for Industrial and Applied Mathematics, 2012. Google Scholar
  4. B Awerbuch and D Peleg. Sparse partitions. In Foundations of Computer Science, 1990. Proceedings., 31st Annual Symposium on, pages 503-513. IEEE, 1990. Google Scholar
  5. Baruch Awerbuch. Complexity of network synchronization. Journal of the ACM (JACM), 32(4):804-823, 1985. Google Scholar
  6. Baruch Awerbuch. Efficient broadcast and light-weighted spanners. manuscript, 1992. Google Scholar
  7. Baruch Awerbuch, Shay Kutten, and David Peleg. Online load balancing in a distributed network. In Proc. 24th ACM Symp. on Theory of Comput, pages 571-580, 1992. Google Scholar
  8. Baruch Awerbuch, Michael Luby, Andrew V Goldberg, and Serge A Plotkin. Network decomposition and locality in distributed computation. In Foundations of Computer Science, 1989., 30th Annual Symposium on, pages 364-369. IEEE, 1989. Google Scholar
  9. Baruch Awerbuch and David Peleg. Routing with polynomial communication-space srade-ff. SIAM Journal on Discrete Mathematics, 5(2):151-162, 1992. Google Scholar
  10. Leonid Barenboim. On the locality of some NP-complete problems. In International Colloquium on Automata, Languages, and Programming, pages 403-415. Springer, 2012. Google Scholar
  11. Leonid Barenboim, Michael Elkin, and Cyril Gavoille. A fast network-decomposition algorithm and its applications to constant-time distributed computation. Theoretical Computer Science, 751:2-23, 2018. Google Scholar
  12. Leonid Barenboim, Michael Elkin, Seth Pettie, and Johannes Schneider. The locality of distributed symmetry breaking. Journal of the ACM (JACM), 63(3):20, 2016. Google Scholar
  13. József Beck. An algorithmic approach to the Lovász local lemma. I. Random Structures & Algorithms, 2(4):343-365, 1991. Google Scholar
  14. Guy E Blelloch, Anupam Gupta, Ioannis Koutis, Gary L Miller, Richard Peng, and Kanat Tangwongsan. Nearly-linear work parallel sdd solvers, low-diameter decomposition, and low-stretch subgraphs. Theory of Computing Systems, 55(3):521-554, 2014. Google Scholar
  15. Janosch Deurer, Fabian Kuhn, and Yannic Maus. Deterministic Distributed Dominating Set Approximation in the CONGEST Model. In Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing, page to appear. ACM, 2019. Google Scholar
  16. Devdatt Dubhashi, Alessandro Mei, Alessandro Panconesi, Jaikumar Radhakrishnan, and Aravind Srinivasan. Fast distributed algorithms for (weakly) connected dominating sets and linear-size skeletons. Journal of Computer and System Sciences, 71(4):467-479, 2005. Google Scholar
  17. Michael Elkin. A faster distributed protocol for constructing a minimum spanning tree. In Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms, pages 359-368. Society for Industrial and Applied Mathematics, 2004. Google Scholar
  18. Michael Elkin and Ofer Neiman. Distributed strong diameter network decomposition. In Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing, pages 211-216. ACM, 2016. Google Scholar
  19. Mohsen Ghaffari. An improved distributed algorithm for maximal independent set. In Proceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms, pages 270-277. Society for Industrial and Applied Mathematics, 2016. Google Scholar
  20. 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
  21. Mohsen Ghaffari and Fabian Kuhn. Derandomizing distributed algorithms with small messages: Spanners and dominating set. In 32nd International Symposium on Distributed Computing (DISC 2018). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2018. Google Scholar
  22. Nathan Linial. Distributive graph algorithms global solutions from local data. In Foundations of Computer Science, 1987., 28th Annual Symposium on, pages 331-335. IEEE, 1987. Google Scholar
  23. Nathan Linial and Michael Saks. Low diameter graph decompositions. Combinatorica, 13(4):441-454, 1993. Google Scholar
  24. Michael Luby. A simple parallel algorithm for the maximal independent set problem. SIAM journal on computing, 15(4):1036-1053, 1986. Google Scholar
  25. Gary L Miller, Richard Peng, and Shen Chen Xu. Parallel graph decompositions using random shifts. In Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures, pages 196-203. ACM, 2013. Google Scholar
  26. Alessandro Panconesi and Aravind Srinivasan. Improved distributed algorithms for coloring and network decomposition problems. In Proceedings of the twenty-fourth annual ACM symposium on Theory of computing, pages 581-592. ACM, 1992. Google Scholar
  27. David Peleg. Distributed computing. SIAM Monographs on discrete mathematics and applications, 5, 2000. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail