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Incremental algorithms for the maximum internal spanning tree problem

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An Erratum to this article was published on 26 September 2022

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Abstract

The maximum internal spanning tree (MIST) problem is utilized to determine a spanning tree in a graph G, with the maximum number of possible internal vertices. The incremental maximum internal spanning tree (IMIST) problem is the incremental version of MIST whose feasible solutions are edge-sequences e1, e2, …, en−1 such that the first k edges form trees for all k ∈ [n − 1]. A solution’s quality is measured using \({\text{max}_{k \in [n - 1]}}\frac{{\text{opt}(G,k)}}{{\left| {\text{In}({T_k})} \right|}}\) with lower being better. Here, opt(G, k) denotes the number of internal vertices in a tree with k edges in G, which has the largest possible number of internal vertices, and ∣In(Tk)∣ is the number of internal vertices in the tree comprising the solution’s first k edges. We first obtained an IMIST algorithm with a competitive ratio of 2, followed by a 12/7-competitive algorithm based on an approximation algorithm for MIST.

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Authors and Affiliations

  1. School of Computer Science and Engineering, Central South University, Changsha, 410083, China

    Xianbin Zhu, Yongjie Yang & Jianxin Wang

  2. Chair of Economic Theory, Saarland University, Saarbrücken, 66123, Germany

    Yongjie Yang

  3. Hunan Provincial Key Laboratory of Intelligent Processing of Big Data on Transportation, Changsha University of Science and Technology, Changsha, 410114, China

    Wenjun Li

Authors
  1. Xianbin Zhu
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  2. Wenjun Li
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  3. Yongjie Yang
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  4. Jianxin Wang
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Correspondence to Jianxin Wang.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61672536, 61502054, 61702557, 61420106009, 61872048, 61872450, 61828205), Hunan Provincial Science and Technology Program (Grant No. 2018WK4001), Natural Science Foundation of Hunan Province (Grant No. 2017JJ3333), Scientific Research Fund of Hunan Provincial Education Department (Grant No. 17C0047), China Postdoctoral Science Foundation (Grant No. 2017M612584), and Postdoctoral Science Foundation of Central South University.

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Zhu, X., Li, W., Yang, Y. et al. Incremental algorithms for the maximum internal spanning tree problem. Sci. China Inf. Sci. 64, 152103 (2021). https://doi.org/10.1007/s11432-019-2630-2

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  • DOI: https://doi.org/10.1007/s11432-019-2630-2

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