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

2025-11-28

AI Summary

This paper investigates leader election in content-agnostic asynchronous pulse networks on non-2-edge-connected graphs, breaking the conventional reliance on 2-edge connectivity. For anonymous networks, it introduces— for the first time—the use of local or global topological knowledge (e.g., diameter, tree structure) to circumvent the inherent impossibility arising from graph symmetry. Theoretically, it establishes that leader election with quiescent termination is feasible on asymmetric trees with message complexity O(n²); on even-diameter trees, knowing only the diameter suffices to reduce message complexity to O(nr). The work uncovers the pivotal role of topological awareness in extremely weak communication models, precisely characterizing the boundary between solvability and unsolvability in terms of topological knowledge. It thus establishes a novel paradigm for distributed coordination under content-free communication.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Multiagent Systems: Other Foundations of Multi Agent Systems
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

The content-oblivious model, introduced by Censor-Hillel, Cohen, Gelles, and Sel (PODC 2022; Distributed Computing 2023), captures an extremely weak form of communication where nodes can only send asynchronous, content-less pulses. Censor-Hillel, Cohen, Gelles, and Sel 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. 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 $O(n^2)$ 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 $mathcal{G} = {P_3, P_5}$, both the 3-path $P_3$ and the 5-path $P_5$ admit a quiescently terminating leader election if nodes know the topology exactly. However, if nodes only know that the underlying topology belongs to $mathcal{G}$, then terminating leader election is impossible.

Problem

• Studying leader election feasibility in content-oblivious communication networks with topology knowledge
• Establishing impossibility results for symmetric graphs despite unique identifiers
• Developing algorithms for trees using network diameter and topology awareness

Innovation

• Using topology knowledge for leader election
• Employing quiescent termination in anonymous networks
• Leveraging network diameter for message efficiency