IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v7y1973i3p287-293.html
   My bibliography  Save this article

Minimax Location of a Facility in an Undirected Tree Graph

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/trsc.7.3.287
    Download Restriction: no
    File URL: https://libkey.io/10.1287/trsc.7.3.287?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Liying Kang & Yukun Cheng, 2010. "The p-maxian problem on block graphs," Journal of Combinatorial Optimization, Springer, vol. 20(2), pages 131-141, August.
    16. 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.
    17. 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.
    18. 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.
    19. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ortrsc:v:7:y:1973:i:3:p:287-293. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.