## Abstract

We provide lower and upper bounds for γ(n), the number of optimal solutions for the two-center problem: "Given a set S of n points in the real plane, find two closed discs whose union contains all of the points such that the radius of the larger disc is minimized." The main result of the paper shows the matching upper and lower bounds for the two-center problem and demonstrates that γ(n) = n.

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

Pages (from-to) | 187-196 |

Number of pages | 10 |

Journal | Computational Geometry: Theory and Applications |

Volume | 14 |

Issue number | 4 |

DOIs | |

State | Published - Dec 27 1999 |

### Bibliographical note

Funding Information:I A conference version of this paper appeared in the Proceedings of the Seventh Canadian Conference on Computational Geometry, Quebec, August 1995, pp. 19–24. ∗Corresponding author. E-mail: [email protected] 1Partially supported by the Center for Computational Sciences of the University of Kentucky.

### Funding

I A conference version of this paper appeared in the Proceedings of the Seventh Canadian Conference on Computational Geometry, Quebec, August 1995, pp. 19–24. ∗Corresponding author. E-mail: [email protected] 1Partially supported by the Center for Computational Sciences of the University of Kentucky.

Funders | Funder number |
---|---|

University of Kentucky |

## Keywords

- 2-center problem
- Combinatorial geometry
- Computational geometry

## ASJC Scopus subject areas

- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics