## 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 (2-dimensional space). 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 L_{∞} metric, and an O(n) time algorithm to solve the 3-dispersion problem in the L_{1} metric. Also, we give an O(n^{2} log n) time algorithm to solve the 3-dispersion problem in the L_{2} metric.

Original language | English |
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Pages (from-to) | 1101-1107 |

Number of pages | 7 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E104A |

Issue number | 9 |

DOIs | |

Publication status | Published - 2021 |

## Keywords

- Algorithms
- Dispersion problem
- Facility location

## ASJC Scopus subject areas

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics