S. Dobrev, R. Kralovic, D. Pardubska:  Leader Election in Extremely Unreliable Rings and Complete Networks

Abstract:  In this paper we investigate deterministic leader election under the simple threshold model of omission dynamic faults: The computation is performed in synchronous steps; if the algorithm sends m messages in one particular step, then at most max (c_G-1,m-1) of them may be lost without any notification to the sender, where c_G is the edge-connectivity of the communication topology. Simple threshold and related models of dynamic faults have been mainly used in the study of information dispersal (broadcasting), while fault-tolerant leader election has been primarily considered in models with static faults. In this paper we combine these lines of research and present efficient algorithms for leader election on rings and complete networks in the simple threshold model. Somewhat surprisingly, obtaining some leader election is rather straightforward even in this harsh model. However, getting an efficient solution working in general case (arbitrary wake-up, unknown n) involves intricate techniques and careful accounting.