Deterministic Leader Election in Anonymous Sensor Networks Without Common Coordinated System

National audienceDans ce papier, nous nous focalisons sur le problème qui consiste à élire un leader dans un réseau de n capteurs anonymes ne partageant aucun système commun de coordonnées. En supposant que lorsque les robots disposent de la propriété de latéralité, nous donnons une caractérisation complète sur les positions des capteurs permettant de distinguer un leader, et ce quelque soit n. Lorsqu'ils ne disposent pas de la propriété de latéralité, nous montrons que cette caractérisation reste vraie si et seulement si n est impair. Ces résultats sont vrais même si les capteurs possèdent une mémoire et une visibilité infinie, sont mobiles et peuvent communiquer entre eux

Gathering in Dynamic Rings

The gathering problem requires a set of mobile agents, arbitrarily positioned at different nodes of a network to group within finite time at the same location, not fixed in advanced. The extensive existing literature on this problem shares the same fundamental assumption: the topological structure does not change during the rendezvous or the gathering; this is true also for those investigations that consider faulty nodes. In other words, they only consider static graphs. In this paper we start the investigation of gathering in dynamic graphs, that is networks where the topology changes continuously and at unpredictable locations. We study the feasibility of gathering mobile agents, identical and without explicit communication capabilities, in a dynamic ring of anonymous nodes; the class of dynamics we consider is the classic 1-interval-connectivity. We focus on the impact that factors such as chirality (i.e., a common sense of orientation) and cross detection (i.e., the ability to detect, when traversing an edge, whether some agent is traversing it in the other direction), have on the solvability of the problem. We provide a complete characterization of the classes of initial configurations from which the gathering problem is solvable in presence and in absence of cross detection and of chirality. The feasibility results of the characterization are all constructive: we provide distributed algorithms that allow the agents to gather. In particular, the protocols for gathering with cross detection are time optimal. We also show that cross detection is a powerful computational element. We prove that, without chirality, knowledge of the ring size is strictly more powerful than knowledge of the number of agents; on the other hand, with chirality, knowledge of n can be substituted by knowledge of k, yielding the same classes of feasible initial configurations