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

We propose a self-stabilizing leader election (SS-LE) protocol on ring networks in the population protocol model. Given a rough knowledge psi = [log n] + O(1) on the population size n, the proposed protocol lets the population reach a safe configuration within O (n(2) logn) 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.