New Competitive Strategies for Searching in UnknownStar - Shaped

We consider searching problems in robotics that a robot has to nd a path to a target by traveling in an unknown star-shaped polygon P. The goal is to minimize the ratio of the distance traveled by the robot to the length of the shortest start-to-target path. Let s be a starting point in P. We rst present a competitive strategy to nd a path from s to the closest kernel point k of P. The length of the path that the robot generates is less than 1 + 2 p 2 (< 3:829) times the distance from s to k. This is superior to the previous ratio 5:331 in 5, 7] and is the rst result to guarantee a searching within three times the lower bound of p 2 5]. Second, given a speciied target t in P, we present a competitive strategy to nd a path from s to t whose length does not exceed 17 times the length of the shortest s-t path. Moreover, we show that no strategies are better than 9-competitive, and thus our ratio is within twice the lower bound.