Minimalist Leader Election Under Weak Communication

TL;DR

This paper introduces a minimalistic, identifier-free leader election protocol suitable for weak communication models, achieving convergence in near-optimal time with minimal assumptions, making it ideal for simple or biological systems.

Contribution

The protocol operates with only six states, requires no prior knowledge, and works under very weak communication assumptions, advancing leader election in minimalistic distributed systems.

Findings

Almost sure convergence to a single leader

Convergence in $O(D^2 \log n)$ rounds

Improved convergence to $O(D \\log n)$ with approximate diameter knowledge

Abstract

We propose a protocol to solve Leader Election within weak communication models such as the beeping model or the stone-age model. Unlike most previous work, our algorithm operates on only six states, does not require unique identifiers, and assumes no prior knowledge of the network's size or topology, i.e., it is uniform. We show that under our protocol, the system almost surely converges to a configuration in which a single node is in a leader state. With high probability, this occurs in fewer than $O(D^2 \log n)$ rounds, where $D$ is the network diameter. We also show that this can be decreased to $O(D \log n)$ when a constant factor approximation of $D$ is known. The main drawbacks of our approach are a $\Tilde{\Omega}(D)$ overhead in the running time compared to algorithms with stronger requirements, and the fact that nodes are unaware of when a single-leader configuration is reached. Nevertheless, the minimal assumptions and natural appeal of our solution make it particularly well-suited for implementation in the simplest distributed systems, especially biological ones.