## 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 language | English |
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Pages (from-to) | 219-228 |

Number of pages | 10 |

Journal | Computational Geometry: Theory and Applications |

Volume | 39 |

Issue number | 3 |

DOIs | |

State | Published - 1 Apr 2008 |

## Keywords

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

## ASJC Scopus subject areas

- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics