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An approximation algorithm for the k-generalized Steiner forest problem

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Abstract

In this paper, we introduce the k-generalized Steiner forest (k-GSF) problem, which is a natural generalization of the k-Steiner forest problem and the generalized Steiner forest problem. In this problem, we are given a connected graph \(G =(V,E)\) with non-negative costs \(c_{e}\) for the edges \(e\in E\), a set of disjoint vertex sets \({\mathcal {V}}=\{V_{1},V_{2},\ldots ,V_{l}\}\) and a parameter \(k\le l\). The goal is to find a minimum-cost edge set \(F\subseteq E\) that connects at least k vertex sets in \({\mathcal {V}}\). Our main work is to construct an \(O(\sqrt{l})\)-approximation algorithm for the k-GSF problem based on a greedy approach and an LP-rounding technique.

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Acknowledgements

The authors would like to thank the referee for giving this paper a careful reading and many valuable comments and useful suggestions. This work was supported by the NSF of China (No. 11971146), the NSF of Hebei Province of China (No. A2019205089, No. A2019205092), Hebei Province Foundation for Returnees (CL201714) and Overseas Expertise Introduction Program of Hebei Auspices (25305008).

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Authors and Affiliations

  1. School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, 050024, People’s Republic of China

    Jiawen Gao, Suogang Gao, Wen Liu & Bo Hou

  2. Department of Computer Science, University of Texas at Dallas, Richardson, TX, 75080, USA

    Weili Wu & Ding-Zhu Du

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  1. Jiawen Gao
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  2. Suogang Gao
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  3. Wen Liu
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  4. Weili Wu
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  5. Ding-Zhu Du
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  6. Bo Hou
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Correspondence to Bo Hou.

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Gao, J., Gao, S., Liu, W. et al. An approximation algorithm for the k-generalized Steiner forest problem. Optim Lett 15, 1475–1483 (2021). https://doi.org/10.1007/s11590-021-01727-y

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