On Sense of Direction and Mobile Agents

An edge-labeled graph is said to have Sense of Direction if the labeling satisfies a particular set of global consistency properties. When the graph represents a system of communicating entities, the presence of sense of direction has been shown to have a strong impact on computability and complexity. Since its introduction, sense of direction has been investigated from various view points, revealing interesting graph theoretical properties and providing useful tools for the design of efficient distributed algorithms; furthermore, its presence allows to solve some otherwise unsolvable problems. Far from being exhausted, the study of sense of direction and other consistency properties of edge-labeled graphs is still filled with interesting questions, open problems, and important new research directions. In this paper, we revisit sense of direction reviewing the main results in the context of message passing point-to-point models, showing its impact in the more recent mobile agents models, and indicating directions for future study.