Exploring trees by teams of asynchronous oblivious robots

A team of identical, oblivious, mobile agents (robots) has to explore an anonymous unoriented tree by visiting all its nodes. Robots start from arbitrary different nodes of the tree and operate in Look-Compute-Move cycles. At the end, every node must be visited by at least one robot, and all robots must stop. In one cycle, a robot takes a snapshot of the current configuration (Look), makes a decision to stay idle or to move to one of its adjacent nodes (Compute), and in the latter case makes an instantaneous move to this neighbor (Move). Cycles are performed asynchronously for each robot. We present an exploration algorithm for arbitrary n-node trees of maximum degree 3 using O(log n/ log log n) robots, and we prove that for some such trees Ω(log n/ log log n) robots are necessary to explore them. We also show that in order to explore some n-node trees of maximum degree 4, Ω(n) robots are necessary. By contrast we show that in order to explore trees that do not have non-trivial automorphisms, 4 robots are always sufficient and often necessary.