Document Open Access Logo

Loosely-Stabilizing Phase Clocks and The Adaptive Majority Problem

Authors Petra Berenbrink, Felix Biermeier, Christopher Hahn, Dominik Kaaser

PDF
Thumbnail PDF

File

LIPIcs.SAND.2022.7.pdf
  • Filesize: 0.84 MB
  • 17 pages

Document Identifiers

Author Details

Petra Berenbrink
  • Universität Hamburg, Germany
Felix Biermeier
  • Universität Hamburg, Germany
Christopher Hahn
  • Universität Hamburg, Germany
Dominik Kaaser
  • Universität Hamburg, Germany

Cite AsGet BibTex

Petra Berenbrink, Felix Biermeier, Christopher Hahn, and Dominik Kaaser. Loosely-Stabilizing Phase Clocks and The Adaptive Majority Problem. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 7:1-7:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.SAND.2022.7

Abstract

We present a loosely-stabilizing phase clock for population protocols. In the population model we are given a system of n identical agents which interact in a sequence of randomly chosen pairs. Our phase clock is leaderless and it requires O(log n) states. It runs forever and is, at any point of time, in a synchronous state w.h.p. When started in an arbitrary configuration, it recovers rapidly and enters a synchronous configuration within O(n log n) interactions w.h.p. Once the clock is synchronized, it stays in a synchronous configuration for at least poly(n) parallel time w.h.p. We use our clock to design a loosely-stabilizing protocol that solves the adaptive variant of the majority problem. We assume that the agents have either opinion A or B or they are undecided and agents can change their opinion at a rate of 1/n. The goal is to keep track which of the two opinions is (momentarily) the majority. We show that if the majority has a support of at least Ω(log n) agents and a sufficiently large bias is present, then the protocol converges to a correct output within O(n log n) interactions and stays in a correct configuration for poly(n) interactions, w.h.p.

Subject Classification

ACM Subject Classification
  • Theory of computation
Keywords
  • Population Protocols
  • Phase Clocks
  • Loose Self-stabilization
  • Clock Synchronization
  • Majority
  • Adaptive

Metrics

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

Related Versions

References

  1. Dan Alistarh, James Aspnes, and Rati Gelashvili. Space-optimal majority in population protocols. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA, pages 2221-2239. SIAM, 2018. URL: https://doi.org/10.1137/1.9781611975031.144.
  2. Dan Alistarh, Bartlomiej Dudek, Adrian Kosowski, David Soloveichik, and Przemyslaw Uznanski. Robust detection in leak-prone population protocols. In DNA Computing and Molecular Programming - 23rd International Conference, DNA, volume 10467 of Lecture Notes in Computer Science, pages 155-171. Springer, 2017. URL: https://doi.org/10.1007/978-3-319-66799-7_11.
  3. Dan Alistarh, Martin Töpfer, and Przemyslaw Uznanski. Comparison dynamics in population protocols. In Avery Miller, Keren Censor-Hillel, and Janne H. Korhonen, editors, PODC '21: ACM Symposium on Principles of Distributed Computing, Virtual Event, Italy, July 26-30, 2021, pages 55-65. ACM, 2021. URL: https://doi.org/10.1145/3465084.3467915.
  4. Talley Amir, James Aspnes, and John Lazarsfeld. Approximate majority with catalytic inputs. In Quentin Bramas, Rotem Oshman, and Paolo Romano, editors, 24th International Conference on Principles of Distributed Systems, OPODIS 2020, December 14-16, 2020, Strasbourg, France (Virtual Conference), volume 184 of LIPIcs, pages 19:1-19:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.OPODIS.2020.19.
  5. Dana Angluin, James Aspnes, Zoë Diamadi, Michael J. Fischer, and René Peralta. Computation in networks of passively mobile finite-state sensors. Distributed Comput., 18(4):235-253, 2006. URL: https://doi.org/10.1007/s00446-005-0138-3.
  6. Dana Angluin, James Aspnes, and David Eisenstat. Stably computable predicates are semilinear. In Proceedings of the Twenty-Fifth Annual ACM Symposium on Principles of Distributed Computing, PODC, pages 292-299. ACM, 2006. URL: https://doi.org/10.1145/1146381.1146425.
  7. Dana Angluin, James Aspnes, and David Eisenstat. Fast computation by population protocols with a leader. Distributed Comput., 21(3):183-199, 2008. URL: https://doi.org/10.1007/s00446-008-0067-z.
  8. Dana Angluin, James Aspnes, and David Eisenstat. A simple population protocol for fast robust approximate majority. Distributed Comput., 21(2):87-102, 2008. URL: https://doi.org/10.1007/s00446-008-0059-z.
  9. Dana Angluin, James Aspnes, David Eisenstat, and Eric Ruppert. The computational power of population protocols. Distributed Comput., 20(4):279-304, 2007. URL: https://doi.org/10.1007/s00446-007-0040-2.
  10. James Aspnes. Clocked population protocols. J. Comput. Syst. Sci., 121:34-48, 2021. URL: https://doi.org/10.1016/j.jcss.2021.05.001.
  11. Luca Becchetti, Andrea E. F. Clementi, and Emanuele Natale. Consensus dynamics: An overview. SIGACT News, 51(1):58-104, 2020. URL: https://doi.org/10.1145/3388392.3388403.
  12. Stav Ben-Nun, Tsvi Kopelowitz, Matan Kraus, and Ely Porat. An o(log^3/2n) parallel time population protocol for majority with o(log n) states. In Proceedings of the ACM Symposium on Principles of Distributed Computing, PODC 2020, Virtual Event, Italy, August 3-7, 2020, page to appear, 2020. Google Scholar
  13. Petra Berenbrink, Felix Biermeier, Christopher Hahn, and Dominik Kaaser. Self-stabilizing phase clocks and the adaptive majority problem. CoRR, abs/2106.13002, 2021. URL: http://arxiv.org/abs/2106.13002.
  14. Petra Berenbrink, Robert Elsässer, Tom Friedetzky, Dominik Kaaser, Peter Kling, and Tomasz Radzik. Time-space trade-offs in population protocols for the majority problem. Distributed Computing, 2020. Google Scholar
  15. Petra Berenbrink, Robert Elsässer, Tom Friedetzky, Dominik Kaaser, Peter Kling, and Tomasz Radzik. Time-space trade-offs in population protocols for the majority problem. Distributed Comput., 34(2):91-111, 2021. URL: https://doi.org/10.1007/s00446-020-00385-0.
  16. Petra Berenbrink, George Giakkoupis, and Peter Kling. Optimal time and space leader election in population protocols. In Proccedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC, pages 119-129. ACM, 2020. URL: https://doi.org/10.1145/3357713.3384312.
  17. Janna Burman, Ho-Lin Chen, Hsueh-Ping Chen, David Doty, Thomas Nowak, Eric E. Severson, and Chuan Xu. Time-optimal self-stabilizing leader election in population protocols. In Avery Miller, Keren Censor-Hillel, and Janne H. Korhonen, editors, PODC '21: ACM Symposium on Principles of Distributed Computing, Virtual Event, Italy, July 26-30, 2021, pages 33-44. ACM, 2021. URL: https://doi.org/10.1145/3465084.3467898.
  18. Anne Condon, Monir Hajiaghayi, David G. Kirkpatrick, and Ján Manuch. Approximate majority analyses using tri-molecular chemical reaction networks. Nat. Comput., 19(1):249-270, 2020. URL: https://doi.org/10.1007/s11047-019-09756-4.
  19. Shlomi Dolev and Jennifer L. Welch. Self-stabilizing clock synchronization in the presence of byzantine faults. J. ACM, 51(5):780-799, September 2004. URL: https://doi.org/10.1145/1017460.1017463.
  20. David Doty, Mahsa Eftekhari, Leszek Gąsieniec, Eric Severson, Grzegorz Stachowiak, and Przemysław Uznański. A time and space optimal stable population protocol solving exact majority, 2022. FOCS 2022, to appear. URL: http://arxiv.org/abs/2106.10201.
  21. David Doty and David Soloveichik. Stable leader election in population protocols requires linear time. Distributed Computing, 31(4):257-271, 2018. URL: https://doi.org/10.1007/s00446-016-0281-z.
  22. Leszek Gasieniec and Grzegorz Stachowiak. Fast space optimal leader election in population protocols. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA, pages 2653-2667. SIAM, 2018. URL: https://doi.org/10.1137/1.9781611975031.169.
  23. Michael Mitzenmacher and Eli Upfal. Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press, 2005. URL: https://doi.org/10.1017/CBO9780511813603.
  24. Yuichi Sudo, Junya Nakamura, Yukiko Yamauchi, Fukuhito Ooshita, Hirotsugu Kakugawa, and Toshimitsu Masuzawa. Loosely-stabilizing leader election in a population protocol model. Theor. Comput. Sci., 444:100-112, 2012. URL: https://doi.org/10.1016/j.tcs.2012.01.007.
  25. Kunal Talwar and Udi Wieder. Balanced allocations: A simple proof for the heavily loaded case. In Automata, Languages, and Programming - 41st International Colloquium, ICALP, volume 8572 of Lecture Notes in Computer Science, pages 979-990. Springer, 2014. URL: https://doi.org/10.1007/978-3-662-43948-7_81.
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 Schloss Dagstuhl - LZI GmbH Imprint Privacy Contact