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Recoverable robust spanning tree problem under interval uncertainty representations

Author

Listed:
  • Mikita Hradovich

    (Wrocław University of Technology)

  • Adam Kasperski

    (Wrocław University of Technology)

  • Paweł Zieliński

    (Wrocław University of Technology)

Abstract

This paper deals with the recoverable robust spanning tree problem under interval uncertainty representations. A strongly polynomial time, combinatorial algorithm for the recoverable spanning tree problem is first constructed. This problem generalizes the incremental spanning tree problem, previously discussed in literature. The algorithm built is then applied to solve the recoverable robust spanning tree problem, under the traditional interval uncertainty representation, in polynomial time. Moreover, the algorithm allows to obtain several approximation results for the recoverable robust spanning tree problem under the Bertsimas and Sim interval uncertainty representation and the interval uncertainty representation with a budget constraint.

Suggested Citation

  • Mikita Hradovich & Adam Kasperski & Paweł Zieliński, 2017. "Recoverable robust spanning tree problem under interval uncertainty representations," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 554-573, August.
    • Handle: RePEc:spr:jcomop:v:34:y:2017:i:2:d:10.1007_s10878-016-0089-6
    DOI: 10.1007/s10878-016-0089-6
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    References listed on IDEAS

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    1. Aissi, Hassene & Bazgan, Cristina & Vanderpooten, Daniel, 2007. "Approximation of min-max and min-max regret versions of some combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 179(2), pages 281-290, June.
    2. Onur Şeref & Ravindra K. Ahuja & James B. Orlin, 2009. "Incremental Network Optimization: Theory and Algorithms," Operations Research, INFORMS, vol. 57(3), pages 586-594, June.
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    Cited by:

    1. Hradovich, Mikita & Kasperski, Adam & Zieliński, Paweł, 2019. "Robust recoverable 0–1 optimization problems under polyhedral uncertainty," European Journal of Operational Research, Elsevier, vol. 278(1), pages 136-148.
    2. Chassein, André & Goerigk, Marc & Kasperski, Adam & Zieliński, Paweł, 2018. "On recoverable and two-stage robust selection problems with budgeted uncertainty," European Journal of Operational Research, Elsevier, vol. 265(2), pages 423-436.
    3. Goerigk, Marc & Lendl, Stefan & Wulf, Lasse, 2022. "Recoverable robust representatives selection problems with discrete budgeted uncertainty," European Journal of Operational Research, Elsevier, vol. 303(2), pages 567-580.

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