Searching and On-line Recognition of Star Shaped Polygons

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We study the problem of on-line searching for a target inside a polygon. In particular, we propose a strategy for finding a target of unknown location in a star-shaped polygon with a competitive ratio of 11.52. We also provide a lower bound of 9 for the competitive ratio of searching in a star-shaped polygon which is close to the upper bound.

A similar task is the on-line recognition of a star-shaped polygon P. Here, the robot travels on a path that allows it to decide whether P is star-shaped or not. We present a strategy with a competitive ratio of 28.85 and give a lower bound of sqrt(82).

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