Document Open Access Logo

Content-Oblivious Leader Election on Rings

Authors Fabian Frei , Ran Gelles , Ahmed Ghazy , Alexandre Nolin

PDF

File

Thumbnail PDF
PDF
LIPIcs.DISC.2024.26.pdf
  • Filesize: 0.9 MB
  • 20 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Content-Oblivious Computation
  • Faulty Communication
  • Leader Election
  • Ring Networks
  • Ring Orientation

Metrics

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

Abstract

In content-oblivious computation, n nodes wish to compute a given task over an asynchronous network that suffers from an extremely harsh type of noise, which corrupts the content of all messages across all channels. In a recent work, Censor-Hillel, Cohen, Gelles, and Sela (Distributed Computing, 2023) showed how to perform arbitrary computations in a content-oblivious way in 2-edge connected networks but only if the network has a distinguished node (called root) to initiate the computation. 
Our goal is to remove this assumption, which was conjectured to be necessary. Achieving this goal essentially reduces to performing a content-oblivious leader election since an elected leader can then serve as the root required to perform arbitrary content-oblivious computations. We focus on ring networks, which are the simplest 2-edge connected graphs. On oriented rings, we obtain a leader election algorithm with message complexity O(n ⋅ ID_max), where ID_max is the maximal assigned ID. As it turns out, this dependency on ID_max is inherent: we show a lower bound of Ω(n log(ID_max/n)) messages for content-oblivious leader election algorithms. We also extend our results to non-oriented rings, where nodes cannot tell which channel leads to which neighbor. In this case, however, the algorithm does not terminate but only reaches quiescence.

Cite As Get BibTex

Fabian Frei, Ran Gelles, Ahmed Ghazy, and Alexandre Nolin. Content-Oblivious Leader Election on Rings. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 26:1-26:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.DISC.2024.26

Author Details

Fabian Frei
  • CISPA Helmholtz Center for Information Security, Saarbrücken, Germany
Ran Gelles
  • Bar-Ilan University, Ramat Gan, Israel
Ahmed Ghazy
  • CISPA Helmholtz Center for Information Security, Saarbrücken, Germany
  • Saarland University, Saarbrücken, Germany
Alexandre Nolin
  • CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

Funding

  • Gelles, Ran: Partially supported by a grant from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel, Grant No. 2020277.

Acknowledgements

R. Gelles would like to thank CISPA - Helmholtz Center for Information Security and MPI - Max Planck Institute for Informatics for hosting him while part of this work was done.

References

  1. Y. Afek and Y. Matias. Elections in anonymous networks. Information and Computation, 113(2):312-330, 1994. URL: https://doi.org/10.1006/inco.1994.1075.
  2. Dana Angluin. Local and global properties in networks of processors (extended abstract). In Proceedings of the Twelfth Annual ACM Symposium on Theory of Computing, STOC '80, pages 82-93, New York, NY, USA, 1980. ACM. URL: https://doi.org/10.1145/800141.804655.
  3. Yagel Ashkenazi, Ran Gelles, and Amir Leshem. Noisy beeping networks. Information and Computation, 289(A):104925, 2022. URL: https://doi.org/10.1016/J.IC.2022.104925.
  4. Hagit Attiya and Marc Snir. Better computing on the anonymous ring. Journal of Algorithms, 12(2):204-238, 1991. URL: https://doi.org/10.1016/0196-6774(91)90002-G.
  5. Hagit Attiya, Marc Snir, and Manfred K. Warmuth. Computing on an anonymous ring. J. ACM, 35(4):845-875, October 1988. URL: https://doi.org/10.1145/48014.48247.
  6. F Thomas Bruss and Colm Art O'cinneide. On the maximum and its uniqueness for geometric random samples. Journal of applied probability, 27(3):598-610, 1990. Google Scholar
  7. James E. Burns. A formal model for message passing systems. Technical report, Computer Science Dept., Indiana Univ., Bloomington, Ind., 1980. TR91. Google Scholar
  8. Keren Censor-Hillel, Shir Cohen, Ran Gelles, and Gal Sela. Distributed computations in fully-defective networks. Distributed Computing, 36(4):501-528, 2023. URL: https://doi.org/10.1007/s00446-023-00452-2.
  9. Keren Censor-Hillel, Ran Gelles, and Bernhard Haeupler. Making asynchronous distributed computations robust to noise. Distributed Computing, 32(5):405-421, October 2019. URL: https://doi.org/10.1007/s00446-018-0343-5.
  10. Ernest Chang and Rosemary Roberts. An improved algorithm for decentralized extrema-finding in circular configurations of processes. Commun. ACM, 22(5):281-283, May 1979. URL: https://doi.org/10.1145/359104.359108.
  11. Alejandro Cornejo and Fabian Kuhn. Deploying wireless networks with beeps. In Distributed Computing, 24th International Symposium, DISC 2010, volume 6343 of LNCS, pages 148-162, 2010, Cambridge, MA, USA, September 13-15, 2010. Proceedings, 2010. Springer. URL: https://doi.org/10.1007/978-3-642-15763-9_15.
  12. Artur Czumaj and Peter Davies. Leader election in multi-hop radio networks. Theoretical Computer Science, 792:2-11, 2019. URL: https://doi.org/10.1016/J.TCS.2019.02.027.
  13. Peter Davies. Optimal message-passing with noisy beeps. In Proceedings of the 2023 ACM Symposium on Principles of Distributed Computing, PODC, pages 300-309, 2023, Orlando, FL, USA, June 19-23, 2023, 2023. ACM. URL: https://doi.org/10.1145/3583668.3594594.
  14. Danny Dolev, Maria Klawe, and Michael Rodeh. An O(n log n) unidirectional distributed algorithm for extrema finding in a circle. Journal of Algorithms, 3(3):245-260, 1982. URL: https://doi.org/10.1016/0196-6774(82)90023-2.
  15. Fabien Dufoulon, Janna Burman, and Joffroy Beauquier. Beeping a deterministic time-optimal leader election. In 32nd International Symposium on Distributed Computing, DISC 2018, volume 121 of LIPIcs, pages 20:1-20:17, New Orleans, LA, USA, October 15-19, 2018, 2018. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPICS.DISC.2018.20.
  16. Fabien Dufoulon, Janna Burman, and Joffroy Beauquier. Can uncoordinated beeps tell stories? In PODC '20: ACM Symposium on Principles of Distributed Computing, pages 408-417, Virtual Event, Italy, August 3-7, 2020, 2020. ACM. URL: https://doi.org/10.1145/3382734.3405699.
  17. M. El-Ruby, J. Kenevan, R. Carlson, and K. Khalil. A linear algorithm for election in ring configuration networks. In Proceedings of the Twenty-Fourth Annual Hawaii International Conference on System Sciences, volume i, pages 117-123 vol.1, Los Alamitos, CA, USA, 1991. IEEE Computer Society. URL: https://doi.org/10.1109/HICSS.1991.183877.
  18. Michael Feldmann, Andreas Padalkin, Christian Scheideler, and Shlomi Dolev. Coordinating amoebots via reconfigurable circuits. Journal of Computational Biology, 29(4):317-343, 2022. URL: https://doi.org/10.1089/cmb.2021.0363.
  19. Paola Flocchini, Evangelos Kranakis, Danny Krizanc, Flaminia L. Luccio, and Nicola Santoro. Sorting and election in anonymous asynchronous rings. Journal of Parallel and Distributed Computing, 64(2):254-265, 2004. URL: https://doi.org/10.1016/j.jpdc.2003.11.007.
  20. Klaus-Tycho Förster, Jochen Seidel, and Roger Wattenhofer. Deterministic leader election in multi-hop beeping networks - (extended abstract). In Distributed Computing - 28th International Symposium, DISC'14, volume 8784 of LNCS, pages 212-226, 2014, Austin, TX, USA, October 12-15, 2014. Proceedings, 2014. Springer. URL: https://doi.org/10.1007/978-3-662-45174-8_15.
  21. Greg N. Frederickson and Nancy A. Lynch. Electing a leader in a synchronous ring. J. ACM, 34(1):98-115, January 1987. URL: https://doi.org/10.1145/7531.7919.
  22. Fabian Frei, Ran Gelles, Ahmed Ghazy, and Alexandre Nolin. Content-oblivious leader election on rings. CoRR, abs/2405.03646, 2024. URL: https://arxiv.org/abs/2405.03646, URL: https://doi.org/10.48550/arXiv.2405.03646.
  23. Ran Gelles. Coding for interactive communication: A survey. Foundations and Trends® in Theoretical Computer Science, 13(1–2):1-157, 2017. URL: https://doi.org/10.1561/0400000079.
  24. Mohsen Ghaffari and Bernhard Haeupler. Near optimal leader election in multi-hop radio networks. In SODA'13, pages 748-766, New Orleans, Louisiana, USA, January 6-8, 2013, 2013. SIAM. URL: https://doi.org/10.1137/1.9781611973105.54.
  25. D. S. Hirschberg and J. B. Sinclair. Decentralized extrema-finding in circular configurations of processors. Commun. ACM, 23(11):627-628, November 1980. URL: https://doi.org/10.1145/359024.359029.
  26. Alon Itai and Michael Rodeh. Symmetry breaking in distributed networks. Information and Computation, 88(1):60-87, 1990. URL: https://doi.org/10.1016/0890-5401(90)90004-2.
  27. Shay Kutten, Peter Robinson, Ming Ming Tan, and Xianbin Zhu. Improved tradeoffs for leader election. In Rotem Oshman, Alexandre Nolin, Magnús M. Halldórsson, and Alkida Balliu, editors, Proceedings of the 2023 ACM Symposium on Principles of Distributed Computing, PODC 2023, Orlando, FL, USA, June 19-23, 2023, pages 355-365. ACM, 2023. URL: https://doi.org/10.1145/3583668.3594576.
  28. Gérard Le Lann. Distributed systems - towards a formal approach. In Bruce Gilchrist, editor, Information Processing, Proceedings of the 7th IFIP Congress 1977, pages 155-160, Toronto, Canada, August 8-12, 1977, 1977. North-Holland. Google Scholar
  29. Gary L. Peterson. An O(n log n) unidirectional algorithm for the circular extrema problem. ACM Trans. Program. Lang. Syst., 4(4):758-762, October 1982. URL: https://doi.org/10.1145/69622.357194.
  30. Nicola Santoro and Peter Widmayer. Distributed function evaluation in the presence of transmission faults. In Tetsuo Asano, Toshihide Ibaraki, Hiroshi Imai, and Takao Nishizeki, editors, Algorithms, International Symposium SIGAL '90, volume 450 of Lecture Notes in Computer Science, pages 358-367, Tokyo, Japan, August 16-18, 1990, 1990. Springer. URL: https://doi.org/10.1007/3-540-52921-7_85.
  31. Violet Syrotiuk and Jan Pachl. A distributed ring orientation algorithm. In International Workshop on Distributed Algorithms (WDAG'87), pages 332-336. Springer Berlin Heidelberg, 1988. URL: https://doi.org/10.1007/BFb0019813.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact