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

TL;DR

This paper refines the analysis of a leader election algorithm in diameter-two networks, reducing message complexity from O(n log^3 n) to O(n log n) while maintaining constant rounds.

Contribution

It provides a tighter analysis of an existing randomized leader election algorithm, significantly reducing message complexity without increasing rounds.

Findings

Message complexity improved to O(n log n)

Algorithm maintains O(1) rounds and high-probability correctness

Refined analysis narrows the gap between lower and upper bounds

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 $\Omega(n)$ 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.