Burman JChen H.-LChen H.-PDoty DNowak TSeverson EXu C.CHEN HO-LIN2022-04-252022-04-252021https://www.scopus.com/inward/record.uri?eid=2-s2.0-85109485150&doi=10.1145%2f3465084.3467898&partnerID=40&md5=8bcc0f6a8bc0ad3b75f414762cb5ec43https://scholars.lib.ntu.edu.tw/handle/123456789/606972We consider the standard population protocol model, where (a priori) indistinguishable and anonymous agents interact in pairs according to uniformly random scheduling. The self-stabilizing leader election problem requires the protocol to converge on a single leader agent from any possible initial configuration. We initiate the study of time complexity of population protocols solving this problem in its original setting: with probability 1, in a complete communication graph. The only previously known protocol by Cai, Izumi, and Wada [Theor. Comput. Syst. 50] runs in expected parallel time Θ(n2) and has the optimal number of n states in a population of n agents. The existing protocol has the additional property that it becomes silent, i.e., the agents' states eventually stop changing. Observing that any silent protocol solving self-stabilizing leader election requires ω(n) expected parallel time, we introduce a silent protocol that uses optimal O(n) parallel time and states. Without any silence constraints, we show that it is possible to solve self-stabilizing leader election in asymptotically optimal expected parallel time of O(log n), but using at least exponential states (a quasi-polynomial number of bits). All of our protocols (and also that of Cai et al.) work by solving the more difficult ranking problem: assigning agents the ranks 1,?,n. ? 2021 Owner/Author.leader electionpopulation protocolsself-stabilizationAsymptotically optimalCommunication graphsInitial configurationLeader Election ProblemQuasi-poly-nomialRandom schedulingRanking problemsStandard populationComputation theoryconference paper10.1145/3465084.34678982-s2.0-85109485150