Low-Communication Self-stabilizing Leader Election in Large Networks

Abstract

This paper makes two contributions: (1) On a completely connected network of n anonymous processes, it presents a synchronous randomized algorithm to solve the weak leader election problem in expected O(1) time using $O(\sqrt{n} \log n)$ messages with high probability, (2) It presents a self-stabilizing algorithm for the strong leader election problem on a completely connected network of processes with unique ids – it stabilizes in expected O(1) number of rounds (or in O(logn) rounds with high probability) using O(n) messages. In doing so, the algorithm also solves the stabilizing unison problem.