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Solving Robust Variants of the Maximum Weighted Independent Set Problem on Trees

Author

Listed:
  • Ana Klobučar

    (Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, 10000 Zagreb, Croatia)

  • Robert Manger

    (Department of Mathematics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia)

Abstract

This paper deals with the maximum weighted independent set (MWIS) problem. We consider several robust variants of the MWIS problem on trees and prove that most of them are NP-hard. We propose a heuristic for solving the considered robust MWIS variants, which is customized for trees. We demonstrate by experiments that our algorithm produces high-quality solutions and runs much faster than a general-purpose optimization software.

Suggested Citation

  • Ana Klobučar & Robert Manger, 2020. "Solving Robust Variants of the Maximum Weighted Independent Set Problem on Trees," Mathematics, MDPI, vol. 8(2), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:285-:d:322901
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    References listed on IDEAS

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    1. Adam Kasperski & Paweł Zieliński, 2016. "Robust Discrete Optimization Under Discrete and Interval Uncertainty: A Survey," International Series in Operations Research & Management Science, in: Michael Doumpos & Constantin Zopounidis & Evangelos Grigoroudis (ed.), Robustness Analysis in Decision Aiding, Optimization, and Analytics, chapter 0, pages 113-143, Springer.
    2. Pop, Petrică C., 2020. "The generalized minimum spanning tree problem: An overview of formulations, solution procedures and latest advances," European Journal of Operational Research, Elsevier, vol. 283(1), pages 1-15.
    3. Aissi, Hassene & Bazgan, Cristina & Vanderpooten, Daniel, 2009. "Min-max and min-max regret versions of combinatorial optimization problems: A survey," European Journal of Operational Research, Elsevier, vol. 197(2), pages 427-438, September.
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