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Efficient Maintenance of Minimum Spanning Trees in Dynamic Weighted Undirected Graphs

Author

Listed:
  • Mao Luo

    (School of Computer Science, Hubei University of Technology, Wuhan 430068, China)

  • Huigang Qin

    (School of Computer Science, Hubei University of Technology, Wuhan 430068, China)

  • Xinyun Wu

    (School of Computer Science, Hubei University of Technology, Wuhan 430068, China)

  • Caiquan Xiong

    (School of Computer Science, Hubei University of Technology, Wuhan 430068, China)

  • Dahai Xia

    (School of Computer Science, Hubei University of Technology, Wuhan 430068, China)

  • Yuanzhi Ke

    (School of Computer Science, Hubei University of Technology, Wuhan 430068, China)

Abstract

This paper presents an algorithm for effectively maintaining the minimum spanning tree in dynamic weighted undirected graphs. The algorithm efficiently updates the minimum spanning tree when the underlying graph structure changes. By identifying the portion of the original tree that can be preserved in the updated tree, our algorithm avoids recalculating the minimum spanning tree from scratch. We provide proof of correctness for the proposed algorithm and analyze its time complexity. In general scenarios, the time complexity of our algorithm is comparable to that of Kruskal’s algorithm. However, the experimental results demonstrate that our algorithm outperforms the approach of recomputing the minimum spanning tree by using Kruskal’s algorithm, especially in medium- and large-scale dynamic graphs where the graph undergoes iterative changes.

Suggested Citation

  • Mao Luo & Huigang Qin & Xinyun Wu & Caiquan Xiong & Dahai Xia & Yuanzhi Ke, 2024. "Efficient Maintenance of Minimum Spanning Trees in Dynamic Weighted Undirected Graphs," Mathematics, MDPI, vol. 12(7), pages 1-22, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1021-:d:1366134
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    References listed on IDEAS

    as
    1. Millington, Tristan & Niranjan, Mahesan, 2021. "Construction of minimum spanning trees from financial returns using rank correlation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    2. Xiaobo Lv & Yan Ma & Xiaofu He & Hui Huang & Jie Yang, 2018. "CciMST: A Clustering Algorithm Based on Minimum Spanning Tree and Cluster Centers," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-14, December.
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