Document Open Access Logo

Self-Stabilizing Clock Synchronization in Probabilistic Networks

Authors Bernadette Charron-Bost, Louis Penet de Monterno

PDF
Thumbnail PDF

File

LIPIcs.DISC.2023.12.pdf
  • Filesize: 0.75 MB
  • 18 pages

Document Identifiers

Author Details

Bernadette Charron-Bost
  • DI ENS, École Normale Supérieure, 75005 Paris, France
Louis Penet de Monterno
  • École polytechnique, IP Paris, 91128 Palaiseau, France

Acknowledgements

We would like to thank Patrick Lambein-Monette, Stephan Merz, and Guillaume Prémel for very useful discussions.

Cite As Get BibTex

Bernadette Charron-Bost and Louis Penet de Monterno. Self-Stabilizing Clock Synchronization in Probabilistic Networks. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 12:1-12:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.DISC.2023.12

Abstract

We consider the fundamental problem of clock synchronization in a synchronous multi-agent system. Each agent holds a clock with an arbitrary initial value, and clocks must eventually indicate the same value, modulo some integer P. A known solution for this problem in dynamic networks is the self-stabilization SAP (for self-adaptive period) algorithm, which uses finite memory and relies solely on the assumption of a finite dynamic diameter in the communication network.
This paper extends the results on this algorithm to probabilistic communication networks: We introduce the concept of strong connectivity with high probability and we demonstrate that in any probabilistic communication network satisfying this hypothesis, the SAP algorithm synchronizes clocks with high probability. The proof of such a probabilistic hyperproperty is based on novel tools and relies on weak assumptions about the probabilistic communication network, making it applicable to a wide range of networks, including the classical push model. We provide an upper bound on time and space complexity.
Building upon previous works by Feige et al. and Pittel, the paper provides solvability results and evaluates the stabilization time and space complexity of SAP in two specific cases of communication topologies.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Dynamic graph algorithms
Keywords
  • Self-stabilization
  • Clock synchronization
  • Probabilistic networks

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Karine Altisen, Stéphane Devismes, Swan Dubois, and Franck Petit. Introduction to distributed self-stabilizing algorithms. Synthesis Lectures on Distributed Computing Theory, 8(1):1-165, 2019. Google Scholar
  2. Dana Angluin, James Aspnes, David Eisenstat, and Eric Ruppert. The computational power of population protocols. Distributed Computing, 20(4):279-304, 2007. URL: https://doi.org/10.1007/s00446-007-0040-2.
  3. Anish Arora, Shlomi Dolev, and Mohamed G. Gouda. Maintaining digital clocks in step. Parallel Processing Letters, 1:11-18, 1991. Google Scholar
  4. Paul Bastide, George Giakkoupis, and Hayk Saribekyan. Self-stabilizing clock synchronization with 1-bit messages. In Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms, SODA, 2021, pages 2154-2173, 2021. Google Scholar
  5. Michael Ben-Or. Another advantage of free choice: Completely asynchronous agreement protocols. In Proceedings of the Second Symposium on Principles of Distributed Computing, pages 27-30, 1983. Google Scholar
  6. Philip. A. Bernstein, Vassos Hadzilacos, and Nathan Goodman. Concurrency Control and Recovery in Database Systems. Addison-Wesley, 1987. Google Scholar
  7. Henrik Björklund, Sven Sandberg, and Sergei Vorobyov. Memoryless determinacy of parity and mean payoff games: a simple proof. Theoretical Computer Science, 310(1-3):365-378, 2004. Google Scholar
  8. Lucas Boczkowski, Amos Korman, and Emanuele Natale. Minimizing message size in stochastic communication patterns: fast self-stabilizing protocols with 3 bits. Distributed Comput., 32(3):173-191, 2019. Google Scholar
  9. Paolo Boldi and Sebastiano Vigna. Universal dynamic synchronous self-stabilization. Distributed Computing, 15(3):137-153, 2002. Google Scholar
  10. Christian Boulinier, Franck Petit, and Vincent Villain. Synchronous vs. asynchronous unison. Algorithmica, 51(1):61-80, 2008. Google Scholar
  11. Bernadette Charron-Bost and Shlomo Moran. The firing squad problem revisited. Theoretical Computer Science, 793:100-112, 2019. Google Scholar
  12. Bernadette Charron-Bost and Louis Penet de Monterno. Self-Stabilizing Clock Synchronization in Dynamic Networks. In 26th International Conference on Principles of Distributed Systems (OPODIS 2022), volume 253 of Leibniz International Proceedings in Informatics (LIPIcs), pages 28:1-28:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. Google Scholar
  13. Bernadette Charron-Bost and Louis Penet de Monterno. Impossibility of self-stabilizing synchronization with bounded memory. ., 2024. Google Scholar
  14. Bernadette Charron-Bost and André Schiper. The Heard-Of model: computing in distributed systems with benign faults. Distributed Computing, 22(1):49-71, 2009. Google Scholar
  15. Herman Chernoff. A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. The Annals of Mathematical Statistics, pages 493-507, 1952. Google Scholar
  16. Michael R Clarkson and Fred B Schneider. Hyperproperties. Journal of Computer Security, 18(6):1157-1210, 2010. Google Scholar
  17. Alejandro Cornejo and Fabian Kuhn. Deploying wireless networks with beeps. In 24th International Symposium on Distributed Computing, DISC 2010, volume 6343 of Lecture Notes on Computer Science, pages 148-162. Springer, 2010. Google Scholar
  18. Shlomi Dolev. Possible and impossible self-stabilizing digital clock synchronization in general graphs. Real Time Syst., 12(1):95-107, 1997. Google Scholar
  19. Shlomi Dolev and Jennifer L. Welch. Self-stabilizing clock synchronization in the presence of byzantine faults. J. ACM, 51(5):780-799, 2004. Google Scholar
  20. Cynthia Dwork, Nancy A. Lynch, and Larry Stockmeyer. Consensus in the presence of partial synchrony. Journal of the ACM, 35(2):288-323, 1988. Google Scholar
  21. Shimon Even and Sergio Rajsbaum. Unison, canon, and sluggish clocks in networks controlled by a synchronizer. Mathematical systems theory, 28(5):421-435, 1995. Google Scholar
  22. Shimon Even and Sergio Rajsbaum. Unison, canon, and sluggish clocks in networks controlled by a synchronizer. Math. Syst. Theory, 28(5):421-435, 1995. Google Scholar
  23. Rui Fan and Nancy Lynch. Gradient clock synchronization. In Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing, pages 320-327, 2004. Google Scholar
  24. Uriel Feige, David Peleg, Prabhakar Raghavan, and Eli Upfal. Randomized broadcast in networks. Random Structures and Algorithms, 1(4):447-460, 1990. Google Scholar
  25. Michael Feldmann, Ardalan Khazraei, and Christian Scheideler. Time- and space-optimal discrete clock synchronization in the beeping model. In 32nd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA, pages 223-233. ACM, 2020. Google Scholar
  26. Alan M Frieze and Geoffrey R Grimmett. The shortest-path problem for graphs with random arc-lengths. Discrete Applied Mathematics, 10(1):57-77, 1985. Google Scholar
  27. Mohamed Gouda and Ted Herman. Stabilizing unison. Inf. Process. Lett., 35(4):171-175, 1990. Google Scholar
  28. Ted Herman and Sukumar Ghosh. Stabilizing phase-clocks. Information Processing Letters, 54(5):259-265, 1995. Google Scholar
  29. Ali Jadbabaie. Natural algorithms in a networked world: technical perspective. Commun. ACM, 55(12):100, 2012. Google Scholar
  30. Ronald Kempe, Joseph Y. Dobra, and Moshe Y. Gehrke. Gossip-based computation of aggregate information. In Proceeding of the 44th IEEE Symposium on Foundations of Computer Science, FOCS, pages 482-491, Cambridge, MA, USA, 2003. Google Scholar
  31. Leslie Lamport. The part-time parliament. ACM Transactions on Computer Systems, 16(2):133-169, May 1998. Google Scholar
  32. Christoph Lenzen, Thomas Locher, and Roger Wattenhofer. Tight bounds for clock synchronization. Journal of the ACM (JACM), 57(2):1-42, 2010. Google Scholar
  33. Boris Pittel. On spreading a rumor. SIAM Journal on Applied Mathematics, 47(1):213-223, 1987. Google Scholar
  34. TK Srikanth and Sam Toueg. Optimal clock synchronization. Journal of the ACM (JACM), 34(3):626-645, 1987. Google Scholar
  35. Steven H. Strogatz. From kuramoto to crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D, 143(1-4):1-20, 2000. Google Scholar
  36. Horst Wegner. Stirling numbers of the second kind and bonferroni’s inequalities. Elemente der Mathematik, 60(3):124-129, 2005. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact