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Guarding Orthogonal Art Galleries Using Sliding Cameras: Algorithmic and Hardness Results

  • Stephane Durocher
  • Saeed Mehrabi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8087)

Abstract

Let P be an orthogonal polygon. Consider a sliding camera that travels back and forth along an orthogonal line segment s ⊆ P as its trajectory. The camera can see a point p ∈ P if there exists a point q ∈ s such that pq is a line segment normal to s that is completely contained in P. In the minimum-cardinality sliding cameras problem, the objective is to find a set S of sliding cameras of minimum cardinality to guard P (i.e., every point in P can be seen by some sliding camera in S) while in the minimum-length sliding cameras problem the goal is to find such a set S so as to minimize the total length of trajectories along which the cameras in S travel.

In this paper, we first settle the complexity of the minimum-length sliding cameras problem by showing that it is polynomial tractable even for orthogonal polygons with holes, answering a question posed by Katz and Morgenstern [9]. Next we show that the minimum-cardinality sliding cameras problem is NP-hard when P is allowed to have holes, which partially answers another question posed by Katz and Morgenstern [9].

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Stephane Durocher
    • 1
  • Saeed Mehrabi
    • 1
  1. 1.Department of Computer ScienceUniversity of ManitobaWinnipegCanada

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