We propose a self-stabilizing leader election (SS-LE) protocol on ring networks in the population protocol model. Given a rough knowledge $\psi = \lceil \log n \rceil + O(1)$ on the population size $n$, the proposed protocol lets the population reach a safe configuration within $O(n^2 \log n)$ steps with high probability starting from any configuration. Thereafter, the population keeps the unique leader forever. Since no protocol solves SS-LE in $o(n^2)$ steps with high probability, the convergence time is near-optimal: the gap is only an $O(\log n)$ multiplicative factor. This protocol uses only $polylog(n)$ states. There exist two state-of-the-art algorithms in current literature that solve SS-LE on ring networks. The first algorithm uses a polynomial number of states and solves SS-LE in $O(n^2)$ steps, whereas the second algorithm requires exponential time but it uses only a constant number of states. Our proposed algorithm provides an excellent middle ground between these two.

翻译：我们在群体协议模型中提出了一种适用于环形网络的自稳定领导者选举（SS-LE）协议。在已知种群规模$n$的粗略估计$\psi = \lceil \log n \rceil + O(1)$的条件下，该协议能够以高概率从任意初始配置出发，在$O(n^2 \log n)$步内使种群达到安全配置。此后，种群将永久保持唯一领导者。由于现有协议无法在$o(n^2)$步内以高概率解决SS-LE问题，因此该收敛时间接近最优：差距仅为$O(\log n)$的乘法因子。该协议仅使用$polylog(n)$个状态。当前文献中有两种最先进的算法可解决环形网络上的SS-LE问题：第一种算法使用多项式个状态，在$O(n^2)$步内完成SS-LE；第二种算法虽仅需常数个状态，但需要指数级时间。我们提出的算法在这两者之间提供了绝佳的折衷方案。