Berenbrink, PetraPetraBerenbrinkElsässer, RobertRobertElsässerGötte, ThorstenThorstenGötteHintze, LukasLukasHintzeKaaser, DominikDominikKaaser2025-11-042025-11-04202545th IEEE International Conference on Distributed Computing Systems, ICDCS 2025https://hdl.handle.net/11420/58476We present a silent, self-stabilizing ranking protocol for the population protocol model of distributed computing, where agents interact in randomly chosen pairs to solve a common task. We are given n anonymous agents, and the goal is to assign each agent a unique rank in {1,...,n}. Given unique ranks, it is straightforward to select a designated leader. Thus, our protocol is a self-stabilizing leader election protocol as well.Ranking requires at least n states per agent; hence, the goal is to minimize the additional number of states, called overhead states. The core of our protocol is a space-efficient but non-self-stabilizing ranking protocol that requires only n+O(logn) states. Our protocol stabilizes in O(n2 logn) interactions w.h.p. and in expectation, using n + O(log2 n) states in total. Our stabilization time is asymptotically optimal (see Burman et al., PODC '21). In comparison to the currently best known ranking protocol by Burman et al., which requires n + Ω(n) states, our result exponentially improves the number of overhead states.enLabelingLeader ElectionPopulation ProtocolsRankingSelf-StabilizationTechnology::600: TechnologyConference Paper10.1109/ICDCS63083.2025.00095Conference Paper