# Time-optimal self-stabilizing leader election in population protocols

arXiv: https://arxiv.org/abs/1907.06068 · HTML: https://mlsanity.com/paper/1907.06068/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2019.

## Built on by (most cited first, 1 of 1)

- [Space-Fluid Adaptive Sampling by Self-Organisation](https://mlsanity.com/paper/2210.17505/) (2022)

## Abstract (arXiv)

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 known protocol by Cai, Izumi, and Wada [Theor. Comput. Syst. 50] runs in expected parallel time Theta(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 Omega(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,ldots,n.