This proposed work is on two algorithmic topics in asynchronous numerics: fault-tolerance and locality. The practical significance of theoretical work in fault-tolerance is often limited because of particular assumptions made about possible fault patterns. In some applications, making unjustifiable assumptions could have grave consequences. The major goals of this research are to develop a basic theory of fault-tolerant communication protocols, that will be free of unnecessary assumptions, and to apply this theory to real network tasks. As a general approach a novel self-stabilization framework is proposed. Self-stabilization is a basic robustness property that enables the system to return to correct operation after an arbitrary pattern of failures. Traditional network management protocols use locality requiring all sites to maintain full information about the network topology. This task becomes very complex in large networks. In a high-speed environment, the required rate of global state change may be much faster than the propagation delay, thus making it impossible to obtain an accurate picture of the global state of the network. Fault- tolerance and locality properties are crucial to ensure graceful degradation of the overall system under conditions of extreme stress. A universal network decomposition approach is proposed, that allows such properties for a variety of network tasks. There is already a wide range of important applications for which this approach has proved to be successful, including network routing, distributed directories, online tracking of mobile users, resource allocation and load balancing, network synchronization, shortest paths, deadlock avoidance, and others. For these tasks our approach yields, for the first time, almost optimal solutions.
