Abstract. 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.
For instance, it is shown in REF that exploration with stop of n-node trees requires a robot with memory size Ω(log log log n) bits, and that exploration with return of n-node trees can be achieved by a robot with O(log 2 n) memory bits.
Tree exploration with little memory
Journal of Algorithms
Computer Science