Leader election and computation of a spanning tree in dynamic distributed networks using local computations and mobile agents

Leader election problem is among the important problems in distributed computing. The continued evolution of distributed systems keeps the distributed computing an open area of research. Distributed algorithms are hard to design and much harder to prove. To make designing distributed algorithm easier, we model this latter with a local computations model. Distributed algorithms are formally presented by rewriting rules. Beyond a formal presentation of these algorithms, local computations theory proposes not only a correctness proof by the use of invariants but also a termination proof by the use of the graph mathematical tool-box. Based on both, the local computations model and the mobile agent paradigms, we present in this paper a distributed algorithm that elects a leader and computes a spanning tree in a dynamic graph. Computations in dynamic graphs can be affected by a set of topological events: we address the appearance and the disappearance of places and communication channels. Our goal is to always maintain a tree by a single leader or a forest of sub-trees where each one has its own leader.