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Solving the 2-rooted mini-max spanning forest problem by branch-and-bound

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  • Mekking, M.
  • Volgenant, A.

Abstract

The 2-rooted mini-max spanning forest problem is to find a spanning forest with two given root nodes on an undirected graph, such that the maximum tree cost in this forest is minimized. We introduce a branch-and-bound algorithm based on selecting nodes. On test instances up to 50 nodes the algorithm gives much better computational results than a known algorithm that is based on selecting edges. Furthermore the new algorithm can easily solve problem instances up to 80 nodes. We consider some alternative and polynomial criteria. Finally we discuss some generalizations, e.g., the problem without given root nodes, i.e., the root nodes have to be chosen.

Suggested Citation

  • Mekking, M. & Volgenant, A., 2010. "Solving the 2-rooted mini-max spanning forest problem by branch-and-bound," European Journal of Operational Research, Elsevier, vol. 203(1), pages 50-58, May.
    • Handle: RePEc:eee:ejores:v:203:y:2010:i:1:p:50-58
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    References listed on IDEAS

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    1. Yamada, Takeo & Takahashi, Hideo & Kataoka, Seiji, 1996. "A heuristic algorithm for the mini-max spanning forest problem," European Journal of Operational Research, Elsevier, vol. 91(3), pages 565-572, June.
    2. Yamada, Takeo & Takahashi, Hideo & Kataoka, Seiji, 1997. "A branch-and-bound algorithm for the mini-max spanning forest problem," European Journal of Operational Research, Elsevier, vol. 101(1), pages 93-103, August.
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    Cited by:

    1. da Cunha, Alexandre Salles & Simonetti, Luidi & Lucena, Abilio, 2015. "Optimality cuts and a branch-and-cut algorithm for the K-rooted mini-max spanning forest problem," European Journal of Operational Research, Elsevier, vol. 246(2), pages 392-399.

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