A Formal Approach for Maintaining Forest Topologies in Dynamic Networks
Résumé
In this paper, we focus on maintaining a forest of spanning trees in dynamic networks. In fact, we propose an approach based on two levels for specifying and proving distributed algorithms in a forest. The rst level allows us to control the dynamic structure of the network by triggering a
maintenance operation when the forest is altered. To do so, we develop a formal pattern using the Event-B method, based on the refinement technique. The proposed pattern relies on the Dynamicity Aware-Graph Relabeling Systems (DA-GRS) which is an existing model for building and maintaining a spanning forest in dynamic networks. It is based on evolving graphs as a powerful model to record the evolution of a network topology. The second level of our approach deals with distributed algorithms which can be applied to spanning trees of the forest. Through an example of a leader election algorithm, we illustrate our pattern. The proof statistics show that our solution can save efforts on specifying as well as proving the correctness of distributed algorithms in a forest topology.