Competitive searching in a generalized street

We consider the problem of a robot which has to find a target in an unknown simple polygon, based only on what it has seen so far. A street is a polygon for which the two boundary chains from start to target are mutually weakly visible. A target inside a street can be found by walking a path that is at most a constant times longer than the shortest path in the street from start to target. We define a strictly larger class of polygons, called generalized streets or G-streets, which are characterized by the property that every point on the boundary of a G-street is visible from a point on a horizontal line segment connecting the two boundary chains. We present an on-line strategy for a robot to find the target in an unknown rectilinear G-street; the length of its path is at most 9 times the length of the shortest path in the L1 metric, and 9.06 times the length of the L2-shortest path. These bounds are optimal.

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