Optimal time self stabilization in dynamic systems

Abstract

A self-stabilizing system is a distributed system which can tolerate any number and any type of faults in the history. After the last fault occurs the system starts to converge to a legitimate behavior. The self-stabilization property is very useful for systems in which processors may malfunction for a while and then recover. When there is a long enough period during which no processor malfunctions the system stabilizes. Dynamic systems are systems in which communication links and processors may fail and recover during normal operation. Such failures could cause partitioning of the system communication graph. The application of self-stabilizing protocols to dynamic systems is natural. Following the last topology change each connected component of the system stabilizes independently. We present time optimal self-stabilizing dynamic protocols for a variety of tasks including: routing, leader election and topology update. The protocol for each of those tasks stabilizes in Θ(d) time, where d is the actual diameter of the system.