Optimum guard covers and m-watchmen routes for restricted polygons

  • Svante Carlsson
  • Bengt J. Nilsson
  • Simeon Ntafos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 519)


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.


Linear Time Algorithm Simple Polygon Supporting Line Event Point Vision Point 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Svante Carlsson
    • 1
  • Bengt J. Nilsson
    • 1
    • 2
  • Simeon Ntafos
    • 3
  1. 1.Department of Computer ScienceLund UniversityLundSweden
  2. 2.Institut für InformatikUniversität FreiburgFreiburgFed. Rep. of Germany
  3. 3.Computer Science ProgramUniversity of Texas at DallasRichardsonU.S.A.

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