Brief Announcement: Minimizing Energy Solves Relative Majority with a Cubic Number of States in Population Protocols

TL;DR

This paper introduces the extsc{Circles} protocol that efficiently solves the relative majority problem in population protocols using only $k^3$ states, significantly improving previous bounds and inspired by energy minimization principles.

Contribution

The paper presents a new protocol that reduces the state complexity from $O(k^7)$ to $k^3$, offering a simpler and more efficient solution for the relative majority problem in population protocols.

Findings

extsc{Circles} protocol always correctly finds the relative majority.

Reduces state complexity from $O(k^7)$ to $k^3$.

Inspired by energy minimization in chemical systems.

Abstract

This paper revisits a fundamental distributed computing problem in the population protocol model. Provided $n$ agents each starting with an input color in $[k]$, the relative majority problem asks to find the predominant color. In the population protocol model, at each time step, a scheduler selects two agents that first learn each other's states and then update their states based on what they learned. We present the \textsc{Circles} protocol that solves the relative majority problem with $k^3$ states. It is always-correct under weakly fair scheduling. Not only does it improve upon the best known upper bound of $O(k^7)$, but it also shows a strikingly simpler design inspired by energy minimization in chemical settings.