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 vision point problem . 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 straight walkable polygons.
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Received June 6, 1996; revised September 12, 1997.
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Carlsson, S., Nilsson, B. Computing Vision Points in Polygons. Algorithmica 24, 50–75 (1999). https://doi.org/10.1007/PL00009271
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DOI: https://doi.org/10.1007/PL00009271