Abstract
We present an on-line strategy for a mobile robot to explore an unknown simple polygon P, so as to output a so-called watchman route such that every interior point of P is visible from at least one point along the route. The length of robot's route is guaranteed to be at most 7 times that of the shortest watchman route that could be computed off-line. This significantly improves upon the previously known 26.5-competitive strategy and confirms a conjecture due to Hoffmann et al. (2001) [10]. Our result is mainly obtained by implementing on-line a known off-line algorithm that approximates the shortest watchman route to a factor of 2.
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