## 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.

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 |
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Title of host publication | 36TH INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE (STACS 2019) |

Editors | Rolf Niedermeier, Christophe Paul |

Publisher | Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik |

Pages | 33:1-33:11 |

Number of pages | 11 |

Volume | 126 |

ISBN (Print) | 978-3-95977-100-9 |

DOIs | |

Publication status | Published - Mar 2019 |

Event | International Symposium on Theoretical Aspects of Computer Science - TU Berlin, Berlin, Germany Duration: 13 Mar 2019 → 16 Mar 2019 Conference number: 36 https://stacs2019.akt.tu-berlin.de/ |

### Publication series

Series | Leibniz International Proceedings in Informatics |
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Volume | 126 |

ISSN | 1868-8969 |

### Conference

Conference | International Symposium on Theoretical Aspects of Computer Science |
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Abbreviated title | STACS |

Country/Territory | Germany |

City | Berlin |

Period | 13/03/19 → 16/03/19 |

Internet address |

## JEL classifications

- c63 - "Computational Techniques; Simulation Modeling"
- c00 - Mathematical and Quantitative Methods: General

## Keywords

- Algorithms
- Complexity
- Facility location
- Graph theory
- Optimization
- algorithms
- complexity
- optimization
- graph theory
- facility location