Distributed Systems and Mobile Computing

The book is about Distributed Systems and Mobile Computing. This is a branch of Computer Science devoted to the study of systems whose components are in different physical locations and have limited communication capabilities. Such components may be static, often organized in a network, or may be able to move in a discrete or continuous environment. The theoretical study of such systems has applications ranging from swarms of mobile robots (e.g., drones) to sensor networks, autonomous intelligent vehicles, the Internet of Things, and crawlers on the Web. The book includes five articles. Two of them are about networks: the first one studies the formation of networks by agents that interact randomly and have the ability to form connections; the second one is a study of clustering models and algorithms. The three remaining articles are concerned with autonomous mobile robots operating in continuous space. One article studies the classical gathering problem, where all robots have to reach a common location, and proposes a fast algorithm for robots that are endowed with a compass but have limited visibility. The last two articles deal with the evacuations problem, where two robots have to locate an exit point and evacuate a region in the shortest possible time

Asynchronous Gathering in a Torus

We consider the gathering problem for asynchronous and oblivious robots that cannot communicate explicitly with each other but are endowed with visibility sensors that allow them to see the positions of the other robots. Most investigations on the gathering problem on the discrete universe are done on ring shaped networks due to the number of symmetric configurations. We extend in this paper the study of the gathering problem on torus shaped networks assuming robots endowed with local weak multiplicity detection. That is, robots cannot make the difference between nodes occupied by only one robot from those occupied by more than one robot unless it is their current node. Consequently, solutions based on creating a single multiplicity node as a landmark for the gathering cannot be used. We present in this paper a deterministic algorithm that solves the gathering problem starting from any rigid configuration on an asymmetric unoriented torus shaped network