On Fractional Dynamic Faults with Threshold

Unlike localized communication failures that occur on a fixed (although a priori unknown) set of links, dynamic faults can occur on any link. Known also as mobile or ubiquitous faults, their presence makes many tasks difficult if not impossible to solve even in synchronous systems. Their analysis and the development of fault-tolerant protocols have been carried out under two main models. In this paper, we introduce a new model for dynamic faults in synchronous distributed systems. This model includes as special cases the existing settings studied in the literature. We focus on the hardest setting of this model, called simple threshold, where to be guaranteed that at least one message is delivered in a time step, the total number of transmitted messages in that time step must reach a threshold T ≤ c(G), where c(G) is the edge connectivity of the network. We investigate the problem of broadcasting under this model for the worst threshold T = c(G) in several classes of graphs as well as in arbitrary networks. We design solution protocols, proving that broadcast is possible even in this harsh environment. We analyze the time costs showing that broadcast can be completed in (low) polynomial time for several networks including rings (with or without knowledge of n), complete graphs (with or without chordal sense of direction), hypercubes (with or without orientation), and constant-degree networks (with or without full topological knowledge).