Leader election in complete networks

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(Nk) and O(N/k), respectively, where log N ≤ k ≤ 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.