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Beyond 2-Edge-Connectivity: Algorithms and Impossibility for Content-Oblivious Leader Election

Authors Yi-Jun Chang , Lyuting Chen , Haoran Zhou

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LIPIcs.ITCS.2026.36.pdf
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ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Asynchronous model
  • fault tolerance
  • quiescent termination

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Abstract

The content-oblivious model, introduced by Censor-Hillel, Cohen, Gelles, and Sela (PODC 2022; Distributed Computing 2023), captures an extremely weak form of communication where nodes can only send asynchronous, content-less pulses. They showed that in 2-edge-connected networks, any distributed algorithm can be simulated in the content-oblivious model, provided that a unique leader is designated a priori. Subsequent works of Frei, Gelles, Ghazy, and Nolin (DISC 2024) and Chalopin et al. (DISC 2025) developed content-oblivious leader election algorithms, first for unoriented rings and then for general 2-edge-connected graphs. These results establish that all graph problems are solvable in content-oblivious, 2-edge-connected networks.
Much less is known about networks that are not 2-edge-connected. Censor-Hillel, Cohen, Gelles, and Sela showed that no non-constant function f(x,y) can be computed correctly by two parties using content-oblivious communication over a single edge, where one party holds x and the other holds y. This seemingly ruled out many natural graph problems on non-2-edge-connected graphs.
In this work, we show that, with the knowledge of network topology G, leader election is possible in a wide range of graphs. Our main contributions are as follows: 
Impossibility: Graphs symmetric about an edge admit no randomized terminating leader election algorithm, even when nodes have unique identifiers and full knowledge of G. 
Leader election algorithms: Trees that are not symmetric about any edge admit a quiescently terminating leader election algorithm with topology knowledge, even in anonymous networks, using O(n²) messages, where n is the number of nodes. Moreover, even-diameter trees admit a terminating leader election given only the knowledge of the network diameter D = 2r, with message complexity O(nr).
Necessity of topology knowledge: In the family of graphs 𝒢 = {P₃, P₅}, both the 3-path P₃ and the 5-path P₅ admit a quiescently terminating leader election if nodes know the topology exactly. However, if nodes only know that the underlying topology belongs to 𝒢, then terminating leader election is impossible.

Cite As Get BibTex

Yi-Jun Chang, Lyuting Chen, and Haoran Zhou. Beyond 2-Edge-Connectivity: Algorithms and Impossibility for Content-Oblivious Leader Election. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 36:1-36:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ITCS.2026.36

Author Details

Yi-Jun Chang
  • National University of Singapore, Singapore
Lyuting Chen
  • National University of Singapore, Singapore
Haoran Zhou
  • National University of Singapore, Singapore

Funding

The research is supported by the Ministry of Education, Singapore, under its Academic Research Fund Tier 1 (24-1323-A0001). Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not reflect the views of the Ministry of Education, Singapore.

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