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Minimax Location of a Facility in an Undirected Tree Graph

Author

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  • G. Y. Handler

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

This paper is addressed to the problem of locating the absolute and vertex centers (minimax criterion) of an undirected tree graph. Based upon a convexity property of the criterion function a very simple and efficient algorithm is offered that locates the minimax point by locating first a maximax point. The minimax is at the mid-point of the maximum path from the maximax point. The vertex center is located simultaneously.

Suggested Citation

  • G. Y. Handler, 1973. "Minimax Location of a Facility in an Undirected Tree Graph," Transportation Science, INFORMS, vol. 7(3), pages 287-293, August.
    • Handle: RePEc:inm:ortrsc:v:7:y:1973:i:3:p:287-293
    DOI: 10.1287/trsc.7.3.287
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    Cited by:

    1. Trung Kien Nguyen & Nguyen Thanh Hung & Huong Nguyen-Thu, 2020. "A linear time algorithm for the p-maxian problem on trees with distance constraint," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 1030-1043, November.
    2. Chunsong Bai & Jun Du, 2024. "The Constrained 2-Maxian Problem on Cycles," Mathematics, MDPI, vol. 12(6), pages 1-9, March.
    3. Esmaeil Afrashteh & Behrooz Alizadeh & Fahimeh Baroughi, 2020. "Optimal approaches for upgrading selective obnoxious p-median location problems on tree networks," Annals of Operations Research, Springer, vol. 289(2), pages 153-172, June.
    4. Becker, Ronald I. & Lari, Isabella & Scozzari, Andrea, 2007. "Algorithms for central-median paths with bounded length on trees," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1208-1220, June.
    5. Wei Ding & Ke Qiu & Yu Zhou & Zhou Ye, 2022. "A sifting-edges algorithm for accelerating the computation of absolute 1-center in graphs," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 905-920, September.
    6. Mulder, H.M. & Pelsmajer, M.J. & Reid, K.B., 2006. "Generalized centrality in trees," Econometric Institute Research Papers EI 2006-16, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    7. 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.
    8. Wolfgang Steitz, 2015. "New Heuristic Approaches for the Bounded-Diameter Minimum Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 151-163, February.
    9. Wei Ding & Ke Qiu, 2017. "An FPTAS for generalized absolute 1-center problem in vertex-weighted graphs," Journal of Combinatorial Optimization, Springer, vol. 34(4), pages 1084-1095, November.
    10. Xinqiang Qian & Xiucui Guan & Junhua Jia & Qiao Zhang & Panos M. Pardalos, 2023. "Vertex quickest 1-center location problem on trees and its inverse problem under weighted $$l_\infty $$ l ∞ norm," Journal of Global Optimization, Springer, vol. 85(2), pages 461-485, February.
    11. Liying Kang & Yukun Cheng, 2010. "The p-maxian problem on block graphs," Journal of Combinatorial Optimization, Springer, vol. 20(2), pages 131-141, August.
    12. Van Huy Pham & Nguyen Chi Tam, 2019. "A combinatorial algorithm for the ordered 1-median problem on cactus graphs," OPSEARCH, Springer;Operational Research Society of India, vol. 56(3), pages 780-789, September.
    13. Oded Berman & Zvi Drezner & George O. Wesolowsky, 2002. "The collection depots location problem on networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(1), pages 15-24, February.
    14. Puerto, Justo & Tamir, Arie & Perea, Federico, 2011. "A cooperative location game based on the 1-center location problem," European Journal of Operational Research, Elsevier, vol. 214(2), pages 317-330, October.
    15. Rainer E. Burkard & Johannes Hatzl, 2010. "Median problems with positive and negative weights on cycles and cacti," Journal of Combinatorial Optimization, Springer, vol. 20(1), pages 27-46, July.
    16. Berman, Oded & Drezner, Zvi & Wesolowsky, George O., 2007. "The transfer point location problem," European Journal of Operational Research, Elsevier, vol. 179(3), pages 978-989, June.
    17. Jafar Fathali & Mehdi Zaferanieh, 2023. "The balanced 2-median and 2-maxian problems on a tree," Journal of Combinatorial Optimization, Springer, vol. 45(2), pages 1-16, March.
    18. Noltemeier, H. & Spoerhase, J. & Wirth, H.-C., 2007. "Multiple voting location and single voting location on trees," European Journal of Operational Research, Elsevier, vol. 181(2), pages 654-667, September.
    19. Wei Ding & Ke Qiu, 2018. "A quadratic time exact algorithm for continuous connected 2-facility location problem in trees," Journal of Combinatorial Optimization, Springer, vol. 36(4), pages 1262-1298, November.
    20. 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.

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