Online exploration outside a convex obstacle
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A watchman route is a path such that a direct line of sight exists between each point in some region and some point along the path. Here, we study watchman routes outside a convex polygon, i.e., in R^2Ø, where O is a convex polygon. We study the problem of a watchman route in an online setting, i.e., in a setting where the watchman is only aware of the vertices of the polygon to which it had a direct line of sight along its route. We present an algorithm guaranteeing a 89.83 competitive ratio relative to the optimal offline path length.
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