Brief announcement: Minimizing energy solves relative majority with a cubic number of states in population protocols Breitkopf, Tom-Lukas Dallot, Julien El-Hayek, Antoine ; https://orcid.org/0000-0003-4268-7368 Schmid, Stefan ddc:000 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 Circles protocol that solves the relative majority problem with k3 states. It is always-correct under weakly fair scheduling. Not only does it improve upon the best known upper bound of O(k7), but it also shows a strikingly simpler design inspired by energy minimization in chemical settings. Association for Computing Machinery 2025 info:eu-repo/semantics/conferenceObject doc-type:conferenceObject text https://research-explorer.ista.ac.at/record/20052 https://research-explorer.ista.ac.at/download/20052/20123 Breitkopf T-L, Dallot J, El-Hayek A, Schmid S. Brief announcement: Minimizing energy solves relative majority with a cubic number of states in population protocols. In: <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>. Association for Computing Machinery; 2025:549-552. doi:<a href="https://doi.org/10.1145/3732772.3733512">10.1145/3732772.3733512</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1145/3732772.3733512 info:eu-repo/semantics/altIdentifier/isbn/9798400718854 info:eu-repo/semantics/altIdentifier/wos/001525534800069 info:eu-repo/semantics/openAccess