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A Note on the Robust 1-Center Problem on Trees

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  • Rainer Burkard
  • Helidon Dollani

Abstract

We consider the robust 1-center problem on trees with uncertainty in vertex weights and edge lengths. The weights of the vertices and the lengths of the edges can take any value in prespecified intervals with unknown distribution. We show that this problem can be solved in O(n 3 log n) time thus improving on Averbakh and Berman's algorithm with time complexity O(n 6 ). For the case when the vertices of the tree have weights equal to 1 we show that the robust 1-center problem can be solved in O(nlog n) time, again improving on Averbakh and Berman's time complexity of O(n 2 log n). Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • Rainer Burkard & Helidon Dollani, 2002. "A Note on the Robust 1-Center Problem on Trees," Annals of Operations Research, Springer, vol. 110(1), pages 69-82, February.
    • Handle: RePEc:spr:annopr:v:110:y:2002:i:1:p:69-82:10.1023/a:1020711416254
    DOI: 10.1023/A:1020711416254
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    Citations

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    Cited by:

    1. Vatsa, Amit Kumar & Jayaswal, Sachin, 2016. "A new formulation and Benders decomposition for the multi-period maximal covering facility location problem with server uncertainty," European Journal of Operational Research, Elsevier, vol. 251(2), pages 404-418.
    2. Conde, Eduardo, 2007. "Minmax regret location-allocation problem on a network under uncertainty," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1025-1039, June.
    3. Vatsa, Amit Kumar & Jayaswal, Sachin, 2015. "A New Formulation and Benders' Decomposition for Multi-period facility Location Problem with Server Uncertainty," IIMA Working Papers WP2015-02-07, Indian Institute of Management Ahmedabad, Research and Publication Department.
    4. Nikulin, Yury, 2006. "Robustness in combinatorial optimization and scheduling theory: An extended annotated bibliography," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 606, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    5. Lu, Chung-Cheng, 2013. "Robust weighted vertex p-center model considering uncertain data: An application to emergency management," European Journal of Operational Research, Elsevier, vol. 230(1), pages 113-121.
    6. Vatsa, Amit Kumar & Jayaswal, Sachin, 2021. "Capacitated multi-period maximal covering location problem with server uncertainty," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1107-1126.
    7. J. Puerto & A. M. Rodríguez-Chía & A. Tamir, 2009. "Minimax Regret Single-Facility Ordered Median Location Problems on Networks," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 77-87, February.
    8. Xu, Jianhua & Johnson, Michael P. & Fischbeck, Paul S. & Small, Mitchell J. & VanBriesen, Jeanne M., 2010. "Robust placement of sensors in dynamic water distribution systems," European Journal of Operational Research, Elsevier, vol. 202(3), pages 707-716, May.
    9. 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.

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