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Locating a Central Hunter on the Plane

Author

Listed:
  • M. Cera

    (University of Seville)

  • J. A. Mesa

    (University of Seville)

  • F. A. Ortega

    (University of Seville)

  • F. Plastria

    (Vrije Universiteit)

Abstract

Protection, surveillance or other types of coverage services of mobile points call for different, asymmetric distance measures than the traditional Euclidean, rectangular or other norms used for fixed points. In this paper, the destinations are mobile points (prey) moving at fixed speeds and directions and the facility (hunter) can capture them using one of two possible strategies: either it is smart, predicting the prey’s movement in order to minimize the time needed to capture it, or it is dumb, following a pursuit curve, by moving at any moment in the direction of the prey. In either case, the hunter location in a plane is sought in order to minimize the maximum time of capture of any prey. An efficient solution algorithm is developed that uses the particular geometry that both versions of this problem possess. In the case of unpredictable movement of prey, a worst-case type solution is proposed, which reduces to the well-known weighted Euclidean minimax location problem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:136:y:2008:i:2:d:10.1007_s10957-007-9293-y
    DOI: 10.1007/s10957-007-9293-y
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    References listed on IDEAS

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    1. Nimrod Megiddo, 1983. "The Weighted Euclidean 1-Center Problem," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 498-504, November.
    2. Donald W. Hearn & James Vijay, 1982. "Efficient Algorithms for the (Weighted) Minimum Circle Problem," Operations Research, INFORMS, vol. 30(4), pages 777-795, August.
    3. Pelegrin, Blas & Michelot, Christian & Plastria, Frank, 1985. "On the uniqueness of optimal solutions in continuous location theory," European Journal of Operational Research, Elsevier, vol. 20(3), pages 327-331, June.
    4. Jack Elzinga & Donald W. Hearn, 1972. "Geometrical Solutions for Some Minimax Location Problems," Transportation Science, INFORMS, vol. 6(4), pages 379-394, November.
    5. Christakis Charalambous, 1982. "Technical Note—Extension of the Elzinga-Hearn Algorithm to the Weighted Case," Operations Research, INFORMS, vol. 30(3), pages 591-594, June.
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    Cited by:

    1. Plastria, F., 2012. "A note towards improved homeland defense," Omega, Elsevier, vol. 40(2), pages 244-248, April.
    2. Teitelbaum, Joshua C., 2013. "Asymmetric empirical similarity," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 346-351.

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