### Abstract

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

Pages (from-to) | 661–669 |

Number of pages | 9 |

Journal | Computational Optimization and Applications |

Volume | 68 |

Issue number | 3 |

DOIs | |

Publication status | Published - Dec 2017 |

### Keywords

- Polyhedral norm
- Exact algorithm
- Single facility location proble
- 1-median
- Rectilinear norm
- Polyhedral norm
- Single facility location problem
- ORDERED MEDIAN PROBLEMS

### Cite this

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*Computational Optimization and Applications*, vol. 68, no. 3, pp. 661–669. https://doi.org/10.1007/s10589-017-9935-4

**An efficient algorithm for the single facility location problem with polyhedral norms and disk-shaped demand regions.** / Berger, Andre; Grigoriev, Alexander; Winokurow, Andrej.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - An efficient algorithm for the single facility location problem with polyhedral norms and disk-shaped demand regions

AU - Berger, Andre

AU - Grigoriev, Alexander

AU - Winokurow, Andrej

N1 - NO DATA USED

PY - 2017/12

Y1 - 2017/12

N2 - The single facility location problem with demand regions seeks for a facility location minimizing the sum of the distances from n demand regions to the facility. The demand regions represent sales markets where the transportation costs are negligible. In this paper, we assume that all demand regions are disks of the same radius, and the distances are measured by a rectilinear norm, e.g. ℓ1 or ℓ∞ . We develop an exact combinatorial algorithm running in time O(nlog^c n) for some c dependent only on the space dimension. The algorithm is generalizable to the other polyhedral norms.

AB - The single facility location problem with demand regions seeks for a facility location minimizing the sum of the distances from n demand regions to the facility. The demand regions represent sales markets where the transportation costs are negligible. In this paper, we assume that all demand regions are disks of the same radius, and the distances are measured by a rectilinear norm, e.g. ℓ1 or ℓ∞ . We develop an exact combinatorial algorithm running in time O(nlog^c n) for some c dependent only on the space dimension. The algorithm is generalizable to the other polyhedral norms.

KW - Polyhedral norm

KW - Exact algorithm

KW - Single facility location proble

KW - 1-median

KW - Rectilinear norm

KW - Polyhedral norm

KW - Single facility location problem

KW - ORDERED MEDIAN PROBLEMS

U2 - 10.1007/s10589-017-9935-4

DO - 10.1007/s10589-017-9935-4

M3 - Article

VL - 68

SP - 661

EP - 669

JO - Computational Optimization and Applications

JF - Computational Optimization and Applications

SN - 0926-6003

IS - 3

ER -