# Polynomial algorithms for center location on spheres

Mordechai Jaeger, Jeffrey B Goldberg

Research output: Contribution to journalArticle

### 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When locating facilities over the earth or in space, a planar location model is no longer valid and we must use a spherical surface.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(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.

Original language English (US) 341-352 12 Naval Research Logistics 44 4 Published - Jun 1997

### Fingerprint

Polynomial Algorithm
Center Problem
Polynomials
Hemisphere
Location Model
Computational complexity
Earth (planet)
NP-complete problem
Valid
Minimise
Demand

### ASJC Scopus subject areas

• Management Science and Operations Research

### Cite this

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

In: Naval Research Logistics, Vol. 44, No. 4, 06.1997, p. 341-352.

Research output: Contribution to journalArticle

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