## Abstract

This paper deals with the problem of locating a maximal cardinality set of obnoxious facilities within a bounded rectangle in the plane such that their pairwise L_{∞}-distance as well as the L_{∞}-distance to a set of already placed demand sites is above a given threshold. We employ techniques and methods from computational geometry to design an optimization algorithm and an efficient frac(1, 2)-approximation algorithm for the problem, and employ the optimization algorithm to design a PTAS based on the shifting strategy [Hochbaum DS, Maass W. Approximation schemes for covering and packing problems in image processing and VLSI. Journal of the ACM 1985;32:130-6]. As a byproduct we improve the algorithm for placing obnoxious facilities given by Katz et al. [Improved algorithms for placing undesirable facilities. Computers & Operations Research 2002;29:1859-72.].

Original language | English |
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Pages (from-to) | 163-171 |

Number of pages | 9 |

Journal | Computers and Operations Research |

Volume | 37 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 2010 |

## Keywords

- Abnoxious multifacility location
- Approximate solution

## ASJC Scopus subject areas

- General Computer Science
- Modeling and Simulation
- Management Science and Operations Research