Digraphs Exploration with Little Memory

Under the robot model, we show that a robot needs Ω(n log d) bits of memory to perform exploration of digraphs with n nodes and maximum out-degree d. We then describe an algorithm that allows exploration of any n-node digraph with maximum out-degree d to be accomplished by a robot with a memory of size O(nd log n) bits. Under the agent model, we show that digraph exploration cannot be achieved by an agent with no memory. We then describe an exploration algorithm for an agent with a constant-size memory, using a whiteboard of size O(log d) bits at every node of out-degree d.