Exploring Unknown Environments

We consider exploration problems where a robot has to construct a complete map of an unknown environment. We assume that the environment is modeled by a directed, strongly connected graph. The robot's task is to visit all nodes and edges of the graph using the minimum number R of edge traversals. Koutsoupias [12] gave a lower bound for R of \Omega\Gamma d 2 m), and Deng and Papadimitriou [9] showed an upper bound of d O(d) m, where m is the number edges in the graph and d is the minimum number of edges that have to be added to make the graph Eulerian. We give the first sub-exponential algorithm for this exploration problem, which achieves an upper bound of d O(log d) m. We also show a matching lower bound of d\Omega\Gamma207 d) m for our algorithm. Additionally, we give lower bounds of 2 \Omega\Gamma d) m, resp. d \Omega\Gamma828 d) m for various other natural exploration algorithms. 1 Introduction Suppose that a robot has to construct a complete map of an unknown envir..