Leader Election in Complete Networks

Abstract

Leader election is a fundamental problem in distributed computing and has a number of applications. This paper studies the problem of leader election in complete asynchronous networks. We present a message-optimal protocol that requires $O(N\log{N})$ messages and $O(N/\log{N})$ time, where $N$ is the number of nodes in the system. The time complexity of this protocol is a significant improvement over currently known protocols for this problem. We also give a family of protocols with message and time complexities $O(N k)$ and $O(N/k)$, respectively, where $\log{N} \leq k \leq N$. Many problems such as spanning-tree construction and computing a global function are equivalent to leader election in terms of their message and time complexities, and therefore our result improves the time complexity of these problems as well.