Why Robots Need Maps

A large group of autonomous, mobile entities e.g. robots initially placed at some arbitrary node of the graph has to jointly visit all nodes (not necessarily all edges) and finally return to the initial position. The graph is not known in advance (an online setting) and robots have to traverse an edge in order to discover new parts (edges) of the graph. The team can locally exchange information, using wireless communication devices. We compare cost of the online and optimal offline algorithm which knows the graph beforehand (competitive ratio). If the cost is the total time of exploraiton, we prove the lower bound of Ω(log k/ log log k) for competitive ratio of any deterministic algorithm (using global communication). This significantly improves the best known constant lower bound. For the cost being the maximal number of edges traversed by a robot (the energy) we present an improved (4− 2/k)-competitive online algorithm for trees.