### Abstract

In this paper we extend the Rectilinear 1-center as follows: Given a set S of n points in the plane, we are interested in locating a facility point f and a rapid transit line (highway) H that together minimize the expression max _{p ∈ S} d _{H} (p,f), where d _{H} (p,f) is the travel time between p and f. A point p ∈ S uses H to reach f if H saves time for p. We solve the problem in O(n ^{2}) or O(nlogn) time, depending on whether or not the highway's length is fixed.

Original language | English |
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Title of host publication | Computational Geometry - XIV Spanish Meeting, EGC 2011, Dedicated to Ferran Hurtado on the Occasion of His 60th Birthday, Revised Selected Papers |

Pages | 155-165 |

Number of pages | 11 |

DOIs | |

Publication status | Published - 2012 Nov 30 |

Externally published | Yes |

Event | 14th Spanish Meeting on Computational Geometry - Alcala de Henares, Spain Duration: 2011 Jun 27 → 2011 Jun 30 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 7579 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 14th Spanish Meeting on Computational Geometry |
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Country | Spain |

City | Alcala de Henares |

Period | 11/6/27 → 11/6/30 |

### Keywords

- Facility location
- Geometric optimization
- Time metric

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Díaz-Báñez, J. M., Korman, C. M., Pérez-Lantero, P., & Ventura, I. (2012). The 1-center and 1-highway problem. In

*Computational Geometry - XIV Spanish Meeting, EGC 2011, Dedicated to Ferran Hurtado on the Occasion of His 60th Birthday, Revised Selected Papers*(pp. 155-165). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7579 LNCS). https://doi.org/10.1007/978-3-642-34191-5_15