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On Guarding Rectilinear Domains

  • Matthew J. Katz
  • Gabriel S. Roisman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4059)

Abstract

We prove that guarding the vertices of a rectilinear polygon P, whether by guards lying at vertices of P, or by guards lying on the boundary of P, or by guards lying anywhere in P, is NP-hard. For the first two proofs (i.e., vertex guards and boundary guards), we construct a reduction from minimum piercing of 2-intervals. The third proof is somewhat simpler; it is obtained by adapting a known reduction from minimum line cover.

We also consider the problem of guarding the vertices of a 1.5D rectilinear terrain by vertex guards. We establish an interesting connection between this problem and the problem of computing a minimum clique cover in chordal graphs. This connection yields a 2-approximation algorithm for the guarding problem.

Keywords

Chordal Graph Simplicial Vertex Clique Cover Rectilinear Polygon Convex Vertex 
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 2006

Authors and Affiliations

  • Matthew J. Katz
    • 1
  • Gabriel S. Roisman
    • 1
  1. 1.Department of Computer ScienceBen-Gurion University of the NegevBeer-ShevaIsrael

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