Watchman route problem

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The Watchman Problem is an optimization problem in computational geometry where the objective is to compute the shortest route a watchman should take to guard an entire area with obstacles given only a map of the area. The challenge is to make sure the watchman peeks behind every corner and to determine the best order in which corners should be visited in. There are polynomial-time solutions but they all suffer from severe numerical problems inherent in the computations.

Note that this is not the same as the museum problem, which is about a similar situation, but with multiple, stationary watchmen.