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Polynomial algorithms for center location on spheres

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  • Mordechai Jaeger
  • Jeff Goldberg

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When locating facilities over the earth or in space, a planar location model is no longer valid and we must use a spherical surface.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 one‐and 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. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 341–352, 1997

Suggested Citation

  • Mordechai Jaeger & Jeff Goldberg, 1997. "Polynomial algorithms for center location on spheres," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(4), pages 341-352, June.
    • Handle: RePEc:wly:navres:v:44:y:1997:i:4:p:341-352
    DOI: 10.1002/(SICI)1520-6750(199706)44:43.0.CO;2-6
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    References listed on IDEAS

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    1. Minnie H. Patel & Deborah L. Nettles & Stuart J. Deutsch, 1993. "A linear‐programming‐based method for determining whether or not n demand points are on a hemisphere," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(4), pages 543-552, June.
    2. Zvi Drezner, 1981. "Technical Note—On Location Dominance on Spherical Surfaces," Operations Research, INFORMS, vol. 29(6), pages 1218-1219, December.
    3. Zvi Drezner & George O. Wesolowsky, 1983. "Minimax and maximin facility location problems on a sphere," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 30(2), pages 305-312, June.
    4. Wen-Hsien Tsai & Maw-Sheng Chern & Tsong-Ming Lin, 1991. "Technical Note—An Algorithm for Determining Whether m Given Demand Points Are on a Hemisphere or Not," Transportation Science, INFORMS, vol. 25(1), pages 91-97, February.
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