Searching Rectilinear Streets Completely

We consider the on-line navigation problem of a robot inside an unknown polygon P. The robot has to find a path from a starting point to an unknown goal point and it is equipped with on-board cameras through which it can get the visibility map of its immediate surroundings. It is known that if P is a street with respect to two points s and t then starting at s the robot can find t with a constant competitive ratio. In this paper we consider the case where the robot is inside a rectilinear street but looks for an arbitrary goal point g instead of t. Furthermore, it may start at some point different from s. We show that in both cases a constant competitive ratio can be achieved and establish lower bounds for this ratio. If the robot starts at s, then our lower and upper bound match, that is, our algorithm is optimal.