Abstract
A watchman, in the terminology of art galleries, is a mobile guard. We consider several watchman and guard problems for different classes of polygons. We introduce the notion of vision spans along a path (route) which provide a natural connection between the (stationary) Art Gallery problem, the m-watchmen problem and the watchman route problem. We prove that finding the minimum number of vision points (i.e., static guards) along a shortest watchman route is NP-hard. We provide a linear time algorithm to compute the best set of static guards in a histogram (Manhattan skyline) polygon. The m-watchmen problem (minimize total length of routes for m watchmen) is NP-hard for simple polygons. We give a Θ(n3+n2m2)-time algorithm to compute the best set of m (moving) watchmen in a histogram.
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