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Content-Oblivious Leader Election on Rings

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

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

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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.

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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.

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