Leader election in complete networks

Abstract

This paper presents protocols for leader election in complete networks. The protocols are message optimal and their time complexities are a significant improvement over currently known protocols for this problem. For asynchronous complete networks with sense of direction, we propose a protocol which requires O(N) messages and O(logN) time. For asynchronous complete network without sense of direction, we show that Ω(N/logN) is a lower bound on the time complexity of any message optimal election protocol and we present a family of protocols which requires O(Nk) messages and O(N/k) time, logN≤k≤N. Our results also improve the time complexity of several other related problems such as spanning tree construction, computing a global function, etc.