On guarding the vertices of rectilinear domains

Matthew J. Katz, Gabriel S. Roisman

Research output: Contribution to journalArticlepeer-review

39 Scopus citations

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. 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.

Original languageEnglish
Pages (from-to)219-228
Number of pages10
JournalComputational Geometry: Theory and Applications
Volume39
Issue number3
DOIs
StatePublished - 1 Apr 2008

Keywords

  • Approximation algorithms
  • Geometric optimization
  • Guarding
  • NP-hardness

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