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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)

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.

Keywords

Linear Time Algorithm Simple Polygon Supporting Line Event Point Vision Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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