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Guarding Monotone Art Galleries with Sliding Cameras in Linear Time

  • Mark de Berg
  • Stephane Durocher
  • Saeed Mehrabi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8881)

Abstract

A sliding camera in an orthogonal polygon \(P\) is a point guard \(g\) that travels back and forth along an orthogonal line segment \(s\) inside \(P\). A point \(p\) in \(P\) is guarded by \(g\) if and only if there exists a point \(q\) on \(s\) such that line segment \(pq\) is normal to \(s\) and contained in \(P\). In the minimum sliding cameras (MSC) problem, the objective is to guard \(P\) with the minimum number of sliding cameras. We give a linear-time dynamic programming algorithm for the MSC problem on \(x\)-monotone orthogonal polygons, improving the 2-approximation algorithm of Katz and Morgenstern (2011). More generally, our algorithm can be used to solve the MSC problem in linear time on simple orthogonal polygons \(P\) for which the dual graph induced by the vertical decomposition of \(P\) is a path. Our results provide the first polynomial-time exact algorithms for the MSC problem on a non-trivial subclass of orthogonal polygons.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Mark de Berg
    • 1
  • Stephane Durocher
    • 2
  • Saeed Mehrabi
    • 2
  1. 1.Department of Mathematics and Computer ScienceTU EindhovenEindhovenThe Netherlands
  2. 2.Department of Computer ScienceUniversity of ManitobaWinnipegCanada

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