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Capacitated Partial Inverse Maximum Spanning Tree Under the Weighted \(l_{\infty }\)-norm

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Combinatorial Optimization and Applications (COCOA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13135))

Abstract

Given an edge weighted graph, and an acyclic edge set, the goal of the partial inverse maximum spanning tree problem is to modify the weight function as small as possible such that there exists a maximum spanning tree with respect to the new weight function containing the given edge set. In this paper, we consider this problem with capacitated constraint under the weighted \(l_{\infty }\)-norm. By studying the properties of the optimal value and a special kind of optimal solutions, combining the algorithm for the decision version of this problem with the Binary search method, we present a strongly polynomial-time algorithm for calculating the optimal value and an optimal solution.

Supported by National Numerical Windtunnel Project (No. NNW2019ZT5-B16), National Natural Science Foundation of China (Nos. 11771013, 11871256, 12071194, U20A2068), and the Basic Research Project of Qinghai (No. 2021-ZJ-703), Zhejiang Provincial Natural Science Foundation of China (No. LD19A010001).

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, Gansu, People’s Republic of China

    Xianyue Li, Ruowang Yang & Heping Zhang

  2. College of Mathematics Physics and Information Engineering, Zhejiang Normal University, Jinhua, 321004, Zhejiang, People’s Republic of China

    Zhao Zhang

Authors
  1. Xianyue Li
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  2. Ruowang Yang
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  3. Heping Zhang
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  4. Zhao Zhang
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Corresponding author

Correspondence to Xianyue Li .

Editor information

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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Li, X., Yang, R., Zhang, H., Zhang, Z. (2021). Capacitated Partial Inverse Maximum Spanning Tree Under the Weighted \(l_{\infty }\)-norm. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Combinatorial Optimization and Applications. COCOA 2021. Lecture Notes in Computer Science(), vol 13135. Springer, Cham. https://doi.org/10.1007/978-3-030-92681-6_31

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  • DOI: https://doi.org/10.1007/978-3-030-92681-6_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92680-9

  • Online ISBN: 978-3-030-92681-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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