Time-optimal self-stabilizing leader election in population protocols [article]

Janna Burman, Ho-Lin Chen, Hsueh-Ping Chen, David Doty, Thomas Nowak, Eric Severson, Chuan Xu
2021 arXiv   pre-print
We 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
more » ... nown protocol by Cai, Izumi, and Wada [Theor. Comput. Syst. 50] runs in expected parallel time Θ(n^2) 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.
arXiv:1907.06068v5 fatcat:uttnh2gwnbgqnolwcjciha3ona