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Minimum diameter cost-constrained Steiner trees

Author

Listed:
  • Wei Ding

    (Zhejiang Water Conservancy and Hydropower College)

  • Guoliang Xue

    (Arizona State University)

Abstract

Given an edge-weighted undirected graph $$G=(V,E,c,w)$$ where each edge $$e\in E$$ has a cost $$c(e)\ge 0$$ and another weight $$w(e)\ge 0$$ , a set $$S\subseteq V$$ of terminals and a given constant $$\mathrm{C}_0\ge 0$$ , the aim is to find a minimum diameter Steiner tree whose all terminals appear as leaves and the cost of tree is bounded by $$\mathrm{C}_0$$ . The diameter of a tree refers to the maximum weight of the path connecting two different leaves in the tree. This problem is called the minimum diameter cost-constrained Steiner tree problem, which is NP-hard even when the topology of the Steiner tree is fixed. In this paper, we deal with the fixed-topology restricted version. We prove the restricted version to be polynomially solvable when the topology is not part of the input and propose a weakly fully polynomial time approximation scheme (weakly FPTAS) when the topology is part of the input, which can find a $$(1+\epsilon )$$ –approximation of the restricted version problem for any $$\epsilon >0$$ with a specific characteristic.

Suggested Citation

  • Wei Ding & Guoliang Xue, 2014. "Minimum diameter cost-constrained Steiner trees," Journal of Combinatorial Optimization, Springer, vol. 27(1), pages 32-48, January.
    • Handle: RePEc:spr:jcomop:v:27:y:2014:i:1:d:10.1007_s10878-013-9611-2
    DOI: 10.1007/s10878-013-9611-2
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    References listed on IDEAS

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    1. Sartaj Sahni, 1977. "General Techniques for Combinatorial Approximation," Operations Research, INFORMS, vol. 25(6), pages 920-936, December.
    2. 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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    Cited by:

    1. Bang Ye Wu & Chen-Wan Lin, 2015. "On the clustered Steiner tree problem," Journal of Combinatorial Optimization, Springer, vol. 30(2), pages 370-386, August.

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