### Abstract

We study a continuous facility location problem on a graph where all edges have unit length and where the facilities may also be positioned in the interior of the edges. The goal is to position as many facilities as possible subject to the condition that any two facilities have at least distance δ from each other. We investigate the complexity of this problem in terms of the rational parameter δ. The problem is polynomially solvable, if the numerator of δ is 1 or 2, while all other cases turn out to be NP-hard.

Original language | English |
---|---|

Place of Publication | Cornell University Library, US |

Publisher | arXiv.org at Cornell University Library |

Number of pages | 13 |

Volume | 1811.08918 |

Publication status | Published - 21 Nov 2018 |

### Publication series

Series | cs.DS |
---|

### JEL classifications

- c00 - Mathematical and Quantitative Methods: General

### Keywords

- Algorithms
- Complexity
- Optimization
- Graph theory
- Facility location

## Cite this

Grigoriev, A., Hartmann, T. A., Lendl, S., & Woeginger, G. J. (2018).

*Dispersing obnoxious facilities on a graph*. arXiv.org at Cornell University Library. cs.DS https://arxiv.org/abs/1811.08918