Self-stabilizing leader election in polynomial steps

We propose a silent self-stabilizing leader election algorithm for bidirectional arbitrary connected identified networks. This algorithm is written in the locally shared memory model under the distributed unfair daemon. It requires no global knowledge on the network. Its stabilization time is in Θ(n3) steps in the worst case, where n is the number of processes. Its memory requirement is asymptotically optimal, i.e., Θ(log⁡n) bits per processes. Its round complexity is of the same order of magnitude - i.e., Θ(n) rounds - as the best existing algorithms designed with similar settings. To the best of our knowledge, this is the first self-stabilizing leader election algorithm for arbitrary identified networks that is proven to achieve a stabilization time polynomial in steps. By contrast, we show that the previous best existing algorithms designed with similar settings stabilize in a non-polynomial number of steps in the worst case.