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We propose a self-stabilizing leader election (SS-LE) protocol on ringnetworks in the population protocol model. Given a rough knowledge $\psi =\lceil \log n \rceil + O(1)$ on the population size $n$, the proposed protocollets the population reach a safe configuration within $O(n^2 \log n)$ stepswith high probability starting from any configuration. Thereafter, thepopulation 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: thegap is only an $O(\log n)$ multiplicative factor. This protocol uses only$polylog(n)$ states. There exist two state-of-the-art algorithms in currentliterature that solve SS-LE on ring networks. The first algorithm uses apolynomial number of states and solves SS-LE in $O(n^2)$ steps, whereas thesecond algorithm requires exponential time but it uses only a constant numberof states. Our proposed algorithm provides an excellent middle ground betweenthese two.

A Near Time-optimal Population Protocol for Self-stabilizing Leader Election on Rings with a Poly-logarithmic Number of States