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A polynomial solvable minimum risk spanning tree problem with interval data

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  • Chen, Xujin
  • Hu, Jie
  • Hu, Xiaodong

Abstract

We propose and study a new model for the spanning tree problem with interval data, the Minimum Risk Spanning Tree (MRST) problem, that finds diverse applications in network design. Given an underlying network G=(V,E), each link e[set membership, variant]E can be established by paying a cost , and accordingly takes a risk of link failure. The MRST problem is to establish a spanning tree T in G of total cost not more than a given constant so that the risk sum over the links in T is minimized. We prove that the MRST problem can be solved in polynomial time, and thus has algorithmic aspect more satisfactory than the NP-hard robust spanning tree problem with interval data.

Suggested Citation

  • Chen, Xujin & Hu, Jie & Hu, Xiaodong, 2009. "A polynomial solvable minimum risk spanning tree problem with interval data," European Journal of Operational Research, Elsevier, vol. 198(1), pages 43-46, October.
    • Handle: RePEc:eee:ejores:v:198:y:2009:i:1:p:43-46
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    References listed on IDEAS

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    1. Montemanni, R. & Gambardella, L. M., 2005. "A branch and bound algorithm for the robust spanning tree problem with interval data," European Journal of Operational Research, Elsevier, vol. 161(3), pages 771-779, March.
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    3. Montemanni, Roberto, 2006. "A Benders decomposition approach for the robust spanning tree problem with interval data," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1479-1490, November.
    4. Refael Hassin, 1992. "Approximation Schemes for the Restricted Shortest Path Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 36-42, February.
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