Presentation and study of some distributed algorithm problems
In this thesis, we first present a study of several problems in the field of distributed algorithms. We provide a formal model that relies on anonymous networks. In this model, we characterize graphs in which it is possible to solve enumeration and leader election problems. This characterization is based on graph homomorphism. We introduce two algorithms with polynomial complexities that improve existing works with exponential complexities. On the other hand, we study the snapshot problem and we introduce the notion of weak snapshot. We show that there exist solutions for this problem in the context of anonymous networks. We present several results about distributed snapshots that deal with checkpoint and rollback recovery, termination detection or the cartography computation of a network. In a practical aspect, we present the conception, the development process and the implementation of these distributed snapshot algorithms within the simulation and visualization software ViSiDiA.