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

2025-07-11

AI Summary

This work addresses the leader election problem in fully faulty asynchronous networks without a pre-designated leader, specifically on arbitrary 2-edge-connected graphs. We propose the first silent, termination-guaranteed, content-agnostic asynchronous leader election algorithm—refuting the long-standing conjecture that a pre-assigned leader is necessary. Our algorithm operates under the pulse communication model, elects the node with the globally minimal ID, and integrates asynchronous message passing with topology-adaptive coordination. It achieves message complexity O(m·N·IDₘᵢₙ), where m is the number of edges, N the number of nodes, and IDₘᵢₙ the smallest identifier; correctness and guaranteed termination are ensured under the sole assumption of 2-edge connectivity. Crucially, this is the first solution enabling faithful simulation of arbitrary distributed algorithms in noise-free asynchronous settings. Thus, it establishes a foundational primitive for fault-tolerant asynchronous distributed computing.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Multiagent Systems: Distributed Problem Solving

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Security and Privacy: Large-scale security measurements

Abstract

Censor-Hillel, Cohen, Gelles, and Sela (PODC 2022 & Distributed Computing 2023) studied fully-defective asynchronous networks, where communication channels may suffer an extreme form of alteration errors, rendering messages completely corrupted. 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 $O(n cdot mathsf{ID}_{max})$, where $n$ is the number of nodes and $mathsf{ID}_{max}$ is the maximum $mathsf{ID}$. 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 an asynchronous content-oblivious leader election algorithm that quiescently terminates in any 2-edge connected network with message complexity $O(m cdot N cdot mathsf{ID}_{min})$, where $m$ is the number of edges, $N$ is a known upper bound on the number of nodes, and $mathsf{ID}_{min}$ is the smallest $mathsf{ID}$. Combined with the previous simulation result, our finding implies that any algorithm from the noiseless setting can be simulated in the fully-defective setting without assuming a preselected leader, entirely refuting the original conjecture.

Problem

• Leader election in 2-edge-connected networks without predesignated leader
• Simulating noiseless algorithms in fully-defective asynchronous networks
• Overcoming content-oblivious computation constraints in 2-edge-connected topologies

Innovation

• Asynchronous content-oblivious leader election algorithm
• Quiescent termination in 2-edge-connected networks
• Message complexity O(m*N*ID_min)