Optimal fault-tolerant distributed algorithms for election in complete networks with a global sense of direction

Abstract

This paper considers the leader election problem (LEP) in asynchronous complete networks with undetectable fail-stop failures. Especially, it is discussed whether presence of a global sense of direction affects the message complexity of LEP in faulty networks. For a complete network of n processors where k processors start the algorithm spontaneously and at most f p (<n/2) processors are faulty, this paper shows(1) the message complexity of LEP is Θ(n+k f p ), if the complete network has a global sense of direction.It is already known that LEP requires Ω(n log k+k f p ) message exchanges, if the complete network has no global sense of direction. Therefore, our result implies that the message complexity of LEP can be greatly reduced by using a global sense of direction in faulty networks as well as in reliable networks. For a complete network with at most f l (<n−1) faulty links (and no faulty processor), this paper also shows the similar result:(2) the message complexity of LEP is Θ(n+k f l +f l log f l ), if the complete network has a global sense of direction.