conference paper published yes Antoine El-Hayek author 888a098e-fcac-11ee-aff7-d347be57b7250000-0003-4268-7368 Robert Elsässer author Stefan Schmid author MoHe department PODC: Symposium on Principles of Distributed Computing The design and evaluation of modern fully dynamic data structures project Static and Dynamic Hierarchical Graph Decompositions project Fast Algorithms for a Reactive Network Layer project We revisit the majority problem in the population protocol communication model, as first studied by Angluin et al. (Distributed Computing 2008). We consider a more general version of this problem known as plurality consensus, which has already been studied intensively in the literature. In this problem, each node in a system of n nodes, has initially one of k different opinions, and they need to agree on the (relative) majority opinion. In particular, we consider the important and intensively studied model of Undecided State Dynamics. Our main contribution is an almost tight lower bound on the stabilization time: we prove that there exists an initial configuration, even with bias \Delta = \omega(\sqrt{n\log n}), where stabilization requires \Omega(kn\log \frac {\sqrt n} {k \log n}) interactions, or equivalently, \Omega(k\log \frac {\sqrt n} {k \log n}) parallel time for any k = o\left(\frac {\sqrt n}{\log n}\right). This bound is tight for any k \le n^{\frac 1 2 - \epsilon}, where \epsilon >0 can be any small constant, as Amir et al.~(PODC'23) gave a O(k\log n) parallel time upper bound for k = O\left(\frac {\sqrt n} {\log ^2 n}\right). https://research-explorer.ista.ac.at/download/20051/20115/2025_PODC_ElHayek.pdf application/pdfno Association for Computing Machinery2025Huatulco, Mexico eng 9798400718854 2505.02765 00152553480006610.1145/3732772.3733505 https://research-explorer.ista.ac.at/record/22281 El-Hayek A, Elsässer R, Schmid S. 2025. An almost tight lower bound for plurality consensus with undecided state dynamics in the population protocol model. Proceedings of the ACM Symposium on Principles of Distributed Computing. PODC: Symposium on Principles of Distributed Computing. A. El-Hayek, R. Elsässer, and S. Schmid, “An almost tight lower bound for plurality consensus with undecided state dynamics in the population protocol model,” in <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>, Huatulco, Mexico, 2025. El-Hayek A, Elsässer R, Schmid S. An almost tight lower bound for plurality consensus with undecided state dynamics in the population protocol model. In: <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>. Association for Computing Machinery; 2025. doi:<a href="https://doi.org/10.1145/3732772.3733505">10.1145/3732772.3733505</a> El-Hayek, Antoine, Robert Elsässer, and Stefan Schmid. “An Almost Tight Lower Bound for Plurality Consensus with Undecided State Dynamics in the Population Protocol Model.” In <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>. Association for Computing Machinery, 2025. <a href="https://doi.org/10.1145/3732772.3733505">https://doi.org/10.1145/3732772.3733505</a>. El-Hayek, A., Elsässer, R., &#38; Schmid, S. (2025). An almost tight lower bound for plurality consensus with undecided state dynamics in the population protocol model. In <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>. Huatulco, Mexico: Association for Computing Machinery. <a href="https://doi.org/10.1145/3732772.3733505">https://doi.org/10.1145/3732772.3733505</a> El-Hayek, Antoine, et al. “An Almost Tight Lower Bound for Plurality Consensus with Undecided State Dynamics in the Population Protocol Model.” <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>, Association for Computing Machinery, 2025, doi:<a href="https://doi.org/10.1145/3732772.3733505">10.1145/3732772.3733505</a>. A. El-Hayek, R. Elsässer, S. Schmid, in:, Proceedings of the ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, 2025. 200512025-07-21T08:16:15Z2026-07-24T12:48:28Z