Abstract
This paper studies a searching problem in an unknown street. A simple polygon [Formula: see text] with two distinguished vertices, [Formula: see text] and [Formula: see text], is called a street if the two boundary chains from [Formula: see text] to [Formula: see text] are mutually weakly visible. We use a mobile robot to locate [Formula: see text] starting from [Formula: see text]. Assume that the robot has a limited sensing capability that can only detect the constructed edges (also called gaps) on the boundary of its visible region, but cannot measure any angle or distance. The robot does not have knowledge of the street in advance. We present a new competitive strategy for this problem and prove that the length of the path generated by the robot is at most 9-times longer than the shortest path. We also propose a matching lower bound to show that our strategy is optimal. Compared with the previous strategy, we further relaxed the restriction that the robot should take a marking device and use the data structure S-GNT. The analysis of our strategy is tight.
Published Version
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