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.

We consider the problem of evacuating some people from an unknown convex region. The people do neither have information about the region boundary nor their positions. We seek competitive strategy that achieves a competitive ratio of the evacuation path over the shortest path. In the scenario of general plane, we propose a strategy SOP for one group, and prove that its competitive ratio is 19.64. And we propose a 14.37-competitive strategy STP for two groups. Also, we present efficient strategies in the scenario of grid network. Furthermore, our strategies can be used for guiding the robot to search the boundary of an unknown region.