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Approximation Algorithm for Stochastic Prize-Collecting Steiner Tree Problem

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Algorithmic Aspects in Information and Management (AAIM 2019)

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Abstract

Steiner tree problem is a typical NP-hard problems in combinatorial optimization, which has comprehensive application background and is a hot topic in recent years. In this paper, we study the stochastic prize-collecting Steiner tree problem. Before the actual requirements materialize, we can choose (purchase) some edges in the first stage. When actual requirements are revealed, drawn from a prespecified probability distribution, then there are more edges may be chosen (purchased) for the actual requirements. The goal is to minimize the sum of the first stage cost, the expected second stage cost and the expected penalty cost. We propose a primal-dual 3-approximation algorithm for the stochastic prize-collecting Steiner tree problem.

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Acknowledgements

The authors are supported by Natural Science Foundation of China (Nos.11871280, 11471003).

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Authors and Affiliations

  1. School of Mathematical Science and Institute of Mathematics, Nanjing Normal University, Nanjing, 210023, Jiangsu, People’s Republic of China

    Jian Sun, Haiyun Sheng & Xiaoyan Zhang

  2. Department of Operations Research and Scientific Computing, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Jian Sun

  3. School of Mathematical Information, Shaoxing University, Shaoxing, 312000, Zhejiang, People’s Republic of China

    Yuefang Sun

Authors
  1. Jian Sun
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  2. Haiyun Sheng
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  3. Yuefang Sun
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  4. Xiaoyan Zhang
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Corresponding author

Correspondence to Xiaoyan Zhang .

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Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

  2. Hefei University of Technology, Hefei, China

    Lian Li

  3. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

    Xiaoming Sun

  4. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

    Jialin Zhang

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Sun, J., Sheng, H., Sun, Y., Zhang, X. (2019). Approximation Algorithm for Stochastic Prize-Collecting Steiner Tree Problem. In: Du, DZ., Li, L., Sun, X., Zhang, J. (eds) Algorithmic Aspects in Information and Management. AAIM 2019. Lecture Notes in Computer Science(), vol 11640. Springer, Cham. https://doi.org/10.1007/978-3-030-27195-4_24

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  • DOI: https://doi.org/10.1007/978-3-030-27195-4_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-27194-7

  • Online ISBN: 978-3-030-27195-4

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