On guarding rectilinear domains

  • Authors:

  • Matthew J. Katz;Gabriel S. Roisman

  • Affiliations:

  • Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel;Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel

  • Venue:
  • SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
  • Year:
  • 2006

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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