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Content-Oblivious Leader Election in 2-Edge-Connected Networks

Authors Jérémie Chalopin , Yi-Jun Chang , Lyuting Chen , Giuseppe A. Di Luna , Haoran Zhou

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ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Asynchronous model
  • fault tolerance
  • quiescent termination

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Abstract

Censor-Hillel, Cohen, Gelles, and Sela (PODC 2022 & Distributed Computing 2023) studied fully-defective asynchronous networks, where communication channels may arbitrarily corrupt messages. The model is equivalent to content-oblivious computation, where nodes communicate solely via pulses. They showed that if the network is 2-edge-connected, then any algorithm for a noiseless setting can be simulated in the fully-defective setting; otherwise, no non-trivial computation is possible in the fully-defective setting. However, their simulation requires a predesignated leader, which they conjectured to be necessary for any non-trivial content-oblivious task.
Recently, Frei, Gelles, Ghazy, and Nolin (DISC 2024) refuted this conjecture for the special case of oriented ring topology. They designed two asynchronous content-oblivious leader election algorithms with message complexity O(n ⋅ ID_{max}), where n is the number of nodes and ID_{max} is the maximum ID. The first algorithm stabilizes in unoriented rings without termination detection. The second algorithm quiescently terminates in oriented rings, thus enabling the execution of the simulation algorithm after leader election. In this work, we present two results: 

General 2-edge-connected topologies: First, we show an asynchronous content-oblivious leader election algorithm that quiescently terminates in any 2-edge-connected network with message complexity O(m ⋅ N ⋅ ID_{min}), where m is the number of edges, N is a known upper bound on the number of nodes, and ID_{min} is the smallest ID. Combined with the above simulation, this result shows that whenever a size bound N is known, any noiseless algorithm can be simulated in the fully-defective model without a preselected leader, fully refuting the conjecture.

Unoriented rings: We then show that the knowledge of N can be dropped in unoriented ring topologies by presenting a quiescently terminating election algorithm with message complexity O(n ⋅ ID_{max}) that matches the previous bound. Consequently, this result constitutes a strict improvement over the previous state of the art and shows that, on rings, fully-defective and noiseless communication are computationally equivalent, with no additional assumptions.

Cite As Get BibTex

Jérémie Chalopin, Yi-Jun Chang, Lyuting Chen, Giuseppe A. Di Luna, and Haoran Zhou. Content-Oblivious Leader Election in 2-Edge-Connected Networks. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 21:1-21:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.DISC.2025.21

Author Details

Jérémie Chalopin
  • Aix Marseille Univ, CNRS, LIS, Marseille, France
Yi-Jun Chang
  • National University of Singapore, Singapore
Lyuting Chen
  • National University of Singapore, Singapore
Giuseppe A. Di Luna
  • DIAG, Sapienza University of Rome, Italy
Haoran Zhou
  • National University of Singapore, Singapore

Funding

This work has been partially supported by ANR project DUCAT (ANR-20-CE48-0006), by the Ministry of Education, Singapore, under its Academic Research Fund Tier 1 (24-1323-A0001), and by the Italian MUR National Recovery and Resilience Plan funded by the European Union - NextGenerationEU through projects SERICS (PE00000014).

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