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On the rectangular p‐center problem

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  • Zvi Drezner

Abstract

The p‐center problem involves finding the best locations for p facilities such that the furthest among n points is as close as possible to one of the facilities. Rectangular (sometimes called rectilinear, Manhattan, or l1) distances are considered. An O(n) algorithm for the 1‐center problem, an O(n) algorithm for the 2‐center problem, and an O(n logn) algorithm for the 3‐center problem are given. Generalizations to general p‐center problems are also discussed.

Suggested Citation

  • Zvi Drezner, 1987. "On the rectangular p‐center problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(2), pages 229-234, April.
    • Handle: RePEc:wly:navres:v:34:y:1987:i:2:p:229-234
    DOI: 10.1002/1520-6750(198704)34:23.0.CO;2-1
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    References listed on IDEAS

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    Cited by:

    1. Xiaozhou He & Zhihui Liu & Bing Su & Yinfeng Xu & Feifeng Zheng & Binhai Zhu, 2019. "Efficient algorithms for computing one or two discrete centers hitting a set of line segments," Journal of Combinatorial Optimization, Springer, vol. 37(4), pages 1408-1423, May.
    2. Sándor P. Fekete & Joseph S. B. Mitchell & Karin Beurer, 2005. "On the Continuous Fermat-Weber Problem," Operations Research, INFORMS, vol. 53(1), pages 61-76, February.
    3. Nicolas Dupin & Frank Nielsen & El-Ghazali Talbi, 2021. "Unified Polynomial Dynamic Programming Algorithms for P-Center Variants in a 2D Pareto Front," Mathematics, MDPI, vol. 9(4), pages 1-30, February.
    4. Abraham, Gyula & Dosa, Gyorgy & Hvattum, Lars Magnus & Olaj, Tomas Attila & Tuza, Zsolt, 2023. "The board packing problem," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1056-1073.

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