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Efficient Algorithms for the (Weighted) Minimum Circle Problem

Author

Listed:
  • Donald W. Hearn

    (University of Florida, Gainesville, Florida)

  • James Vijay

    (University of Florida, Gainesville, Florida)

Abstract

The (weighted) minimum covering circle problem is a well-known single facility location problem used in emergency facility models. This paper introduces a classification scheme, based on fundamental mathematical programming concepts, for algorithms which solve both weighted and unweighted versions. One result of this classification is proof that a recently developed method is identical to one developed in the nineteenth century. Also, within the classification scheme, efficient new algorithms are given for the weighted problem. The results of some extensive computational tests identify the (empirically) fastest methods.

Suggested Citation

  • Donald W. Hearn & James Vijay, 1982. "Efficient Algorithms for the (Weighted) Minimum Circle Problem," Operations Research, INFORMS, vol. 30(4), pages 777-795, August.
    • Handle: RePEc:inm:oropre:v:30:y:1982:i:4:p:777-795
    DOI: 10.1287/opre.30.4.777
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    Citations

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    Cited by:

    1. O Berman & Z Drezner, 2003. "A probabilistic one-centre location problem on a network," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(8), pages 871-877, August.
    2. Drezner, Zvi & Guyse, Jeffery, 1999. "Application of decision analysis techniques to the Weber facility location problem," European Journal of Operational Research, Elsevier, vol. 116(1), pages 69-79, July.
    3. M. Cera & J. A. Mesa & F. A. Ortega & F. Plastria, 2008. "Locating a Central Hunter on the Plane," Journal of Optimization Theory and Applications, Springer, vol. 136(2), pages 155-166, February.
    4. Piyush Kumar & E. Alper Yıldırım, 2009. "An Algorithm and a Core Set Result for the Weighted Euclidean One-Center Problem," INFORMS Journal on Computing, INFORMS, vol. 21(4), pages 614-629, November.
    5. Mark E. Cawood & P. M. Dearing, 2024. "The weighted Euclidean one-center problem in $${\mathbb {R}}^n$$ R n," Computational Optimization and Applications, Springer, vol. 89(2), pages 553-574, November.
    6. Okabe, Atsuyuki & Suzuki, Atsuo, 1997. "Locational optimization problems solved through Voronoi diagrams," European Journal of Operational Research, Elsevier, vol. 98(3), pages 445-456, May.
    7. P. Dearing & Andrea Smith, 2013. "A dual algorithm for the minimum covering weighted ball problem in $${\mathbb{R}^n}$$," Journal of Global Optimization, Springer, vol. 55(2), pages 261-278, February.
    8. Zvi Drezner & G. O. Wesolowsky, 1991. "Facility location when demand is time dependent," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(5), pages 763-777, October.
    9. 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.
    10. Elshaikh, Abdalla & Salhi, Said & Nagy, Gábor, 2015. "The continuous p-centre problem: An investigation into variable neighbourhood search with memory," European Journal of Operational Research, Elsevier, vol. 241(3), pages 606-621.
    11. Zvi Drezner, 1987. "On the rectangular p‐center problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(2), pages 229-234, April.
    12. Gass, Saul I. & Roy, Pallabi Guha, 2003. "The compromise hypersphere for multiobjective linear programming," European Journal of Operational Research, Elsevier, vol. 144(3), pages 459-479, February.
    13. P. M. Dearing & Pietro Belotti & Andrea M. Smith, 2016. "A primal algorithm for the weighted minimum covering ball problem in $$\mathbb {R}^n$$ R n," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 466-492, July.
    14. Blanco, Víctor & Puerto, Justo, 2021. "Covering problems with polyellipsoids: A location analysis perspective," European Journal of Operational Research, Elsevier, vol. 289(1), pages 44-58.

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