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A Linear-Time Algorithm for Maxisum Facility Location on Tree Networks

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  • S. S. Ting

    (The Johns Hopkins University, Baltimore, Maryland)

Abstract

This paper treats a topic in “obnoxious facility location,” namely the problem of locating a single facility in an n -vertex tree network so as to maximize the sum of its weighted distances from the vertices. It is shown that use of a suitable data structure permits a solution algorithm with computational effort O ( n ), an improvement over the O ( n 2 ) required by a previously indicated procedure.

Suggested Citation

  • S. S. Ting, 1984. "A Linear-Time Algorithm for Maxisum Facility Location on Tree Networks," Transportation Science, INFORMS, vol. 18(1), pages 76-84, February.
    • Handle: RePEc:inm:ortrsc:v:18:y:1984:i:1:p:76-84
    DOI: 10.1287/trsc.18.1.76
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    Cited by:

    1. 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.
    2. Welch, S. B. & Salhi, S., 1997. "The obnoxious p facility network location problem with facility interaction," European Journal of Operational Research, Elsevier, vol. 102(2), pages 302-319, October.
    3. Mehdi Zaferanieh & Jafar Fathali, 2012. "Finding a core of a tree with pos/neg weight," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(2), pages 147-160, October.
    4. 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.
    5. Liying Kang & Yukun Cheng, 2010. "The p-maxian problem on block graphs," Journal of Combinatorial Optimization, Springer, vol. 20(2), pages 131-141, August.
    6. 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.
    7. Rainer Burkard & Jafar Fathali, 2007. "A polynomial method for the pos/neg weighted 3-median problem on a tree," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(2), pages 229-238, April.
    8. Elisabeth Gassner, 2008. "The inverse 1-maxian problem with edge length modification," Journal of Combinatorial Optimization, Springer, vol. 16(1), pages 50-67, July.
    9. Batta, Rajan & Lejeune, Miguel & Prasad, Srinivas, 2014. "Public facility location using dispersion, population, and equity criteria," European Journal of Operational Research, Elsevier, vol. 234(3), pages 819-829.

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