How to learn an unknown environment

The authors consider the problem faced by a newborn that must explore and learn an unknown room with obstacles in it. They seek algorithms that achieve a bounded ratio of the worst-case distance traversed in order to see all visible points of the environment (thus creating a map), divided by the optimum distance needed to verify the map. The situation is complicated by the fact that the latter offline problem (optimally verifying a map) is NP-hard and thus must be solved approximately. Although the authors show that there is no such competitive algorithm for general obstacle courses, they give a competitive algorithm for the case of a polygonal room with a bounded number of obstacles in it