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(n 3+n 2 m 2)-time algorithm to compute the best set of m (moving) watchmen in a histogram.
The work of the second author was supported by the Deutsche Forschungsgemeinschaft under Grant No. Ot 64/5-4.
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© 1991 Springer-Verlag Berlin Heidelberg
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Carlsson, S., Nilsson, B.J., Ntafos, S. (1991). Optimum guard covers and m-watchmen routes for restricted polygons. In: Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1991. Lecture Notes in Computer Science, vol 519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028276
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DOI: https://doi.org/10.1007/BFb0028276
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