### Abstract

When locating facilities over the earth or in space, a planar location model is no longer valid and we must use a spherical surface. In this article, we consider the oneand two-center problems on a sphere that contains n demand points. The problem is to locate facilities to minimize the maximum distance from any demand point to the closest facility. We present an O(n) algorithm for the one-center problem when a hemisphere contains all demand points and also give an O(n) algorithm for determining whether or not the hemisphere property holds. We present an O(n^{3} log n) algorithm for the two-center problem for arbitrarily located demand points. Finally, we show that for general p, the p center on a sphere problem is NP-hard.

Original language | English (US) |
---|---|

Pages (from-to) | 341-352 |

Number of pages | 12 |

Journal | Naval Research Logistics |

Volume | 44 |

Issue number | 4 |

State | Published - Jun 1997 |

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### ASJC Scopus subject areas

- Management Science and Operations Research

### Cite this

*Naval Research Logistics*,

*44*(4), 341-352.

**Polynomial algorithms for center location on spheres.** / Jaeger, Mordechai; Goldberg, Jeffrey B.

Research output: Contribution to journal › Article

*Naval Research Logistics*, vol. 44, no. 4, pp. 341-352.

}

TY - JOUR

T1 - Polynomial algorithms for center location on spheres

AU - Jaeger, Mordechai

AU - Goldberg, Jeffrey B

PY - 1997/6

Y1 - 1997/6

N2 - When locating facilities over the earth or in space, a planar location model is no longer valid and we must use a spherical surface. In this article, we consider the oneand two-center problems on a sphere that contains n demand points. The problem is to locate facilities to minimize the maximum distance from any demand point to the closest facility. We present an O(n) algorithm for the one-center problem when a hemisphere contains all demand points and also give an O(n) algorithm for determining whether or not the hemisphere property holds. We present an O(n3 log n) algorithm for the two-center problem for arbitrarily located demand points. Finally, we show that for general p, the p center on a sphere problem is NP-hard.

AB - When locating facilities over the earth or in space, a planar location model is no longer valid and we must use a spherical surface. In this article, we consider the oneand two-center problems on a sphere that contains n demand points. The problem is to locate facilities to minimize the maximum distance from any demand point to the closest facility. We present an O(n) algorithm for the one-center problem when a hemisphere contains all demand points and also give an O(n) algorithm for determining whether or not the hemisphere property holds. We present an O(n3 log n) algorithm for the two-center problem for arbitrarily located demand points. Finally, we show that for general p, the p center on a sphere problem is NP-hard.

UR - http://www.scopus.com/inward/record.url?scp=0031168845&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031168845&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031168845

VL - 44

SP - 341

EP - 352

JO - Naval Research Logistics

JF - Naval Research Logistics

SN - 0894-069X

IS - 4

ER -