On the Complexity of a Self-Stabilizing Spanning Tree Algorithm for Large Scale Systems

Many large scale systems, like grids and structured peer to peer systems, operate on a constrained topology. Since underlying networks do not expose the real topology to the applications, an algorithm should build and maintain a virtual topology for the application. This algorithm has to bootstrap the system and react to the arrival and departures of processes. In a previous article, we introduced a computing model designed for scalability in which we gave a self-stabilizing algorithm that builds a spanning tree. At that time, we provided a proof of stabilization and performance measurements of a prototypal implementation. In this work, we present a probabilistic method to evaluate the theoretical performances of algorithms in this model, and provide a probabilistic analysis of the convergence time of the algorithm.