The optimal way for looking around a corner

摘要

Let two walls form a wedge of angle less than 180/spl deg/. At one of the walls, a robot is located, facing the corner where the walls meet. The robot's task is to eye the other wall. To this end, it can freely move around in the area outside the wedge. Suppose the robot does not know the angle of the wedge. How should it move to minimize path length? It is shown that there is a strategy which guarantees that, for any possible value of the angle, the length of the path the robot walks before it can look around the corner is bounded by the length of the shortest path to do so, times the constant c /spl ap/ 1.21218. It is proved that the strategy is optimal in that no smaller competitive factor than c can be achieved. A simple formula is given for the robot to find the optimal path.