Toward Optimality: A Tighter Analysis of Message Complexity for Leader Election in Diameter-Two Networks

2026-04-20

AI Summary

This work addresses the problem of optimizing message complexity for leader election in synchronous networks of diameter two. Building upon the randomized algorithm of Chatterjee et al., the authors conduct a refined analysis by introducing more precise probabilistic modeling and combinatorial optimization techniques. This enables a restructured characterization of the message-passing process and a tighter derivation of the complexity upper bound. As a result, while preserving O(1) communication rounds and high-probability correctness, the message complexity is significantly improved from O(n log³ n) to O(n log n). This advancement substantially narrows the gap with the theoretical lower bound of Ω(n), establishing the current state-of-the-art message complexity guarantee for this model.

Technology Category

Reasoning under Uncertainty: Stochastic OptimizationPlanning, Routing, and Scheduling: Scheduling under UncertaintyKnowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystemsSecurity and Privacy: Large-scale security measurements

Abstract

We study the message complexity of leader election in synchronous networks of diameter two. Our main contribution is a refined analysis of the randomized algorithm proposed by Chatterjee et al. [DC, 2020]. In their work, the authors established a lower bound of $Ω(n)$ messages ($n$ is the number of nodes in the network) and presented a randomized algorithm that elects a leader in ${O}(1)$ rounds using $O(n \log^3 n)$ messages with high probability. In this paper, we improve their $\polylog n$ gap in the message bound by providing a tighter analysis of their algorithm, reducing the message complexity to $O(n\log n)$, while preserving the $O(1)$-round complexity and high-probability correctness guarantee.

Problem

• leader election
• message complexity
• diameter-two networks
• synchronous networks
• randomized algorithm

Innovation

• leader election
• message complexity
• diameter-two networks
• randomized algorithm
• tighter analysis