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A polynomial method for the pos/neg weighted 3-median problem on a tree

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  • Rainer Burkard
  • Jafar Fathali

Abstract

Let a connected undirected graph G = (V, E) be given. In the classical p-median problem we want to find a set X containing p points in G such that the sum of weighted distances from X to all vertices in V is minimized. We consider the semi-obnoxious case where every vertex has either a positive or negative weight. In this case we have two different objective functions: the sum of the minimum weighted distances from X to all vertices and the sum of the weighted minimum distances. In this paper we show that for the case p = 3 an optimal solution for the second model in a tree can be found in O(n 5 ) time. If the 3-median is restricted to vertices or if the tree is a path then the complexity can be reduced to O(n 3 ). Copyright Springer-Verlag 2007

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:65:y:2007:i:2:p:229-238
    DOI: 10.1007/s00186-006-0121-1
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    References listed on IDEAS

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    1. 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.
    2. A. J. Goldman, 1971. "Optimal Center Location in Simple Networks," Transportation Science, INFORMS, vol. 5(2), pages 212-221, May.
    3. Richard L. Church & Robert S. Garfinkel, 1978. "Locating an Obnoxious Facility on a Network," Transportation Science, INFORMS, vol. 12(2), pages 107-118, May.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. B. Jayalakshmi & Alok Singh, 2017. "A hybrid artificial bee colony algorithm for the p-median problem with positive/negative weights," OPSEARCH, Springer;Operational Research Society of India, vol. 54(1), pages 67-93, March.

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