### Abstract

Given a set P of n points on which facilities can be placed and an integer k, we want to place k facilities on some points so that the minimum distance between facilities is maximized. The problem is called the k-dispersion problem. In this paper we consider the 3-dispersion problem when P is a set of points on a plane. Note that the 2-dispersion problem corresponds to the diameter problem. We give an O(n) time algorithm to solve the 3-dispersion problem in the (forumala presented). metric, and an O(n) time algorithm to solve the 3-dispersion problem in the (forumala presented) metric. Also we give an (forumala presented) time algorithm to solve the 3-dispersion problem in the (forumala presented) metric.

Original language | English |
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Title of host publication | Computing and Combinatorics - 25th International Conference, COCOON 2019, Proceedings |

Editors | Ding-Zhu Du, Zhenhua Duan, Cong Tian |

Publisher | Springer Verlag |

Pages | 291-300 |

Number of pages | 10 |

ISBN (Print) | 9783030261757 |

DOIs | |

Publication status | Published - 2019 Jan 1 |

Event | 25th International Computing and Combinatorics Conference, COCOON 2019 - Xi'an, China Duration: 2019 Jul 29 → 2019 Jul 31 |

### 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 | 11653 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 25th International Computing and Combinatorics Conference, COCOON 2019 |
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Country | China |

City | Xi'an |

Period | 19/7/29 → 19/7/31 |

### Keywords

- Dispersion problem
- Facility location

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Computing and Combinatorics - 25th International Conference, COCOON 2019, Proceedings*(pp. 291-300). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11653 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-26176-4_24