Derandomizing Distributed Algorithms with Small Messages: Spanners and Dominating Set

Authors Mohsen Ghaffari, Fabian Kuhn



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Author Details

Mohsen Ghaffari
  • ETH Zurich, Switzerland
Fabian Kuhn
  • University of Freiburg, Germany

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Mohsen Ghaffari and Fabian Kuhn. Derandomizing Distributed Algorithms with Small Messages: Spanners and Dominating Set. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 29:1-29:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.DISC.2018.29

Abstract

This paper presents improved deterministic distributed algorithms, with O(log n)-bit messages, for some basic graph problems. The common ingredient in our results is a deterministic distributed algorithm for computing a certain hitting set, which can replace the random part of a number of standard randomized distributed algorithms. This deterministic hitting set algorithm itself is derived using a simple method of conditional expectations. As one main end-result of this derandomized hitting set, we get a deterministic distributed algorithm with round complexity 2^O(sqrt{log n * log log n}) for computing a (2k-1)-spanner of size O~(n^{1+1/k}). This improves considerably on a recent algorithm of Grossman and Parter [DISC'17] which needs O(n^{1/2-1/k} * 2^k) rounds. We also get a 2^O(sqrt{log n * log log n})-round deterministic distributed algorithm for computing an O(log^2 n)-approximation of minimum dominating set; all prior algorithms for this problem were either randomized or required large messages.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Distributed Algorithms
  • Derandomization
  • Spanners
  • Dominating Set

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References

  1. Noga Alon and Joel H Spencer. The probabilistic method. John Wiley &Sons, 2004. Google Scholar
  2. Matti Åstrand and Jukka Suomela. Fast distributed approximation algorithms for vertex cover and set cover in anonymous networks. In Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures, pages 294-302. ACM, 2010. Google Scholar
  3. B. Awerbuch, AV Goldberg, M. Luby, and S. Plotkin. Network decomposition and locality in distributed computation. In FOCS, pages 364-369, 1989. Google Scholar
  4. Baruch Awerbuch. Complexity of network synchronization. Journal of the ACM (JACM), 32(4):804-823, 1985. Google Scholar
  5. Baruch Awerbuch and David Peleg. Sparse partitions. In Proc. IEEE Symp. on Foundations of Computer Science (FOCS), pages 503-513, 1990. Google Scholar
  6. 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
  7. Leonid Barenboim, Michael Elkin, and Cyril Gavoille. A fast network-decomposition algorithm and its applications to constant-time distributed computation. Theoretical Computer Science, 2016. Google Scholar
  8. Surender Baswana and Sandeep Sen. A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs. Random Structures &Algorithms, 30(4):532-563, 2007. Google Scholar
  9. Keren Censor-Hillel, Merav Parter, and Gregory Schwartzman. Derandomizing local distributed algorithms under bandwidth restrictions. In 31 International Symposium on Distributed Computing, 2017. Google Scholar
  10. Bilel Derbel and Cyril Gavoille. Fast deterministic distributed algorithms for sparse spanners. In International Colloquium on Structural Information and Communication Complexity, pages 100-114. Springer, 2006. Google Scholar
  11. Bilel Derbel, Cyril Gavoille, and David Peleg. Deterministic distributed construction of linear stretch spanners in polylogarithmic time. In International Symposium on Distributed Computing, pages 179-192. Springer, 2007. Google Scholar
  12. Bilel Derbel, Cyril Gavoille, David Peleg, and Laurent Viennot. On the locality of distributed sparse spanner construction. In Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing, pages 273-282. ACM, 2008. Google Scholar
  13. Bilel Derbel, Mohamed Mosbah, and Akka Zemmari. Sublinear fully distributed partition with applications. Theory of Computing Systems, 47(2):368-404, 2010. Google Scholar
  14. Paul Erdős. Some problems in graph theory. In STUDIA SIC MATH. HUNGAR. Citeseer, 1966. Google Scholar
  15. M. Ghaffari and F. Kuhn. Derandomizing distributed algorithms with small messages: Spanners and dominating set. Technical Report 285, U. of Freiburg, Dept. of Computer Science, 2018. URL: http://tr.informatik.uni-freiburg.de/reports/report285/report00285.pdf.
  16. Mohsen Ghaffari. An improved distributed algorithm for maximal independent set. In Pro. ACM-SIAM Symp. on Discrete Algorithms (SODA), 2016. Google Scholar
  17. Mohsen Ghaffari, David G Harris, and Fabian Kuhn. On derandomizing local distributed algorithms. arXiv preprint arXiv:1711.02194, 2017. Google Scholar
  18. Ofer Grossman and Merav Parter. Improved deterministic distributed construction of spanners. In 31 International Symposium on Distributed Computing, 2017. Google Scholar
  19. Lujun Jia, Rajmohan Rajaraman, and Torsten Suel. An efficient distributed algorithm for constructing small dominating sets. Distributed Computing, 15(4):193-205, 2002. Google Scholar
  20. Ken-Ichi Kawarabayashi and Gregory Schwartzman. Adapting local sequential algorithms to the distributed setting. arXiv preprint arXiv:1711.10155, 2017. Google Scholar
  21. Fabian Kuhn, Thomas Moscibroda, and Roger Wattenhofer. Local computation: Lower and upper bounds. J. ACM, 63(2):17:1-17:44, mar 2016. Google Scholar
  22. Fabian Kuhn and Roger Wattenhofer. Constant-time distributed dominating set approximation. In Proc. ACM Symp. on Principles of Distributed Computing (PODC), pages 25-32, 2003. Google Scholar
  23. Christoph Lenzen and Roger Wattenhofer. Minimum dominating set approximation in graphs of bounded arboricity. In International Symposium on Distributed Computing, pages 510-524. Springer, 2010. Google Scholar
  24. Nathan Linial. Distributive graph algorithms global solutions from local data. In Proc. IEEE Symp. on Foundations of Computer Science (FOCS), pages 331-335. IEEE, 1987. Google Scholar
  25. Michael Luby. Removing randomness in parallel computation without a processor penalty. Journal of Computer and System Sciences, 47(2):250-286, 1993. Google Scholar
  26. Moni Naor and Larry Stockmeyer. What can be computed locally? SIAM Journal on Computing, 24(6):1259-1277, 1995. Google Scholar
  27. Alessandro Panconesi and Aravind Srinivasan. Improved distributed algorithms for coloring and network decomposition problems. In Proc. ACM Symp. on Theory of Computing (STOC), pages 581-592. ACM, 1992. Google Scholar
  28. David Peleg. Distributed Computing: A Locality-sensitive Approach. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2000. Google Scholar
  29. David Peleg and Jeffrey D Ullman. An optimal synchronizer for the hypercube. SIAM Journal on computing, 18(4):740-747, 1989. Google Scholar
  30. Jeanette P Schmidt, Alan Siegel, and Aravind Srinivasan. Chernoff-hoeffding bounds for applications with limited independence. SIAM J. on Discrete Math., 8(2):223-250, 1995. Google Scholar
  31. Vijay V Vazirani. Approximation algorithms. Springer Science &Business Media, 2013. Google Scholar
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