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An Approximation Algorithm for the B-prize-collecting Multicut Problem in Trees

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Theory and Applications of Models of Computation (TAMC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13571))

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Abstract

In this paper, we consider the B-prize-collecting multicut problem in trees. In this problem, we are given a tree \(T=(V,E)\), a set of k source-sink pairs \(\mathcal {P}=\{(s_1,t_1),(s_2,t_2),\ldots , (s_k,t_k)\}\) and a profit bound B. Every edge \(e\in E\) has a cost \(c_e\), and every source-sink pair \((s_j,t_j)\in \mathcal {P}\) has a profit \(p_j\) and a penalty \(\pi _j\). This problem is to find a multicut \(M\subseteq E\) such that the total cost, which consists of the total cost of the edges in M and the total penalty of the pairs still connected after removing M, is minimized and the total profit of the disconnected pairs by removing M is at least B. Based on the primal-dual scheme, we present an \((\frac{8}{3}+ \epsilon )\)-approximation algorithm by carefully increasing the penalty, where \(\epsilon \) is any fixed positive number.

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Acknowledgement

The work is supported in part by the National Natural Science Foundation of China [No. 12071417].

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Authors and Affiliations

  1. School of Information Science and Engineering, Yunnan University, Kunming, China

    Xiaofei Liu

  2. School of Mathematics and Statistics, Yunnan University, Kunming, China

    Weidong Li

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  1. Xiaofei Liu
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  2. Weidong Li
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Correspondence to Xiaofei Liu .

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Editors and Affiliations

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

    Ding-Zhu Du

  2. University of New Brunswick, Fredericton, NB, Canada

    Donglei Du

  3. Tianjin University of Technology, Tianjin, China

    Chenchen Wu

  4. Beijing University of Technology, Beijing, China

    Dachuan Xu

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Liu, X., Li, W. (2022). An Approximation Algorithm for the B-prize-collecting Multicut Problem in Trees. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Theory and Applications of Models of Computation. TAMC 2022. Lecture Notes in Computer Science, vol 13571. Springer, Cham. https://doi.org/10.1007/978-3-031-20350-3_21

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  • DOI: https://doi.org/10.1007/978-3-031-20350-3_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-20349-7

  • Online ISBN: 978-3-031-20350-3

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