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 16] gave a lower bound for R of (d2m), and Deng and Papadimitriou 12] showed an upper bound of dO(d)m, where m is the number of 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 rst sub-exponential algorithm for this exploration problem, which achieves an upper bound of dO(logd)m. We also show a matching lower bound of d (log d)m for our algorithm. Additionally, we give lower bounds of 2 (d)m, resp. d (log d)m for various other natural exploration algorithms. Key words. directed graph, exploration algorithm AMS subject classi cations. 05C20, 68Q20, 68Q25, 68R10

• Type: Conference
• Year: 1997
• Where: STOC
• Authors: Susanne Albers, Monika Rauch Henzinger
• Keywords: Algorithms, Exploration Problem, Lower Bounds, STOC 1997, Upper Bound