Polynomial algorithms for center location on spheres

Mordechai Jaeger, Jeff 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When locating facilities over the earth or in space, a planar location model is no longer valid and we must use a spherical surface.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 languageEnglish (US)
Pages (from-to)341-352
Number of pages12
JournalNaval Research Logistics
Volume44
Issue number4
DOIs
StatePublished - Jun 1997

ASJC Scopus subject areas

  • Modeling and Simulation
  • Ocean Engineering
  • Management Science and Operations Research

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