Gathering Six Oblivious Robots on Anonymous Symmetric Rings

A recent model for robot-based computing systems makes use of identical, memoryless, and mobile robots placed on nodes of anonymous graphs. Robots operate in Look-Compute-Move cycles; in one cycle, a robot takes a snapshot of the current robots disposal on the entire ring (Look), takes a decision whether to stay idle or to move to one of its adjacent nodes (Compute), and in the latter case makes a move to this neighbor (Move). Cycles are performed asynchronously for each robot. We consider the case of six robots placed on the nodes of an anonymous ring in such a way they constitute a symmetric placement with respect to one single axis of symmetry, and we ask whether there exists a strategy that allows the robots to gather at one node. This is the first case left open after a series of papers dealing with the gathering of oblivious robots on anonymous rings. As long as the gathering is feasible, we provide a new distributed approach that guarantees a positive answer to the posed question.