Computing Vision Points in Polygons

Abstract. We consider a restricted version of the art gallery problem within simple polygons in which the guards are required to lie on a given one-dimensional object, a watchman route. We call this problem the visionpointproblem . We prove the following: • The original art gallery problem is NP-hard for the very restricted class of street polygons. • The vision point problem can be solved efficiently for the class of street polygons. • A linear time algorithm for the vision point problem exists for the subclass of street polygons called straightwalkable polygons.

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