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Minimum Spanning Tree Method for Sparse Graphs

Author

Listed:
  • Xianchao Wang
  • Shaoyi Li
  • Changhui Hou
  • Guoming Zhang
  • Ganesh Ghorai

Abstract

The minimum spanning tree (MST) is widely used in planning the most economical network. The algorithm for finding the MST of a connected graph is essential. In this paper, a new algorithm for finding MST is proposed based on a deduced theorem of MST. The algorithm first sorts the edges in the graph according to their weight, from large to small. Next, on the premise of ensuring the connectivity of the graph, it deletes the edges in this order until the number of edges of the graph is equal to the number of vertexes minus 1. Finally, the remaining graph is an MST. This algorithm is equivalent to an inverse Kruskal algorithm. For sparse graphs, the proposed algorithm has higher efficiency than the Kruskal algorithm. Experiments and analysis verify the effectiveness of the algorithm proposed in this paper. The algorithm provides a better choice for finding the MST of the sparse graph.

Suggested Citation

  • Xianchao Wang & Shaoyi Li & Changhui Hou & Guoming Zhang & Ganesh Ghorai, 2023. "Minimum Spanning Tree Method for Sparse Graphs," Mathematical Problems in Engineering, Hindawi, vol. 2023, pages 1-6, February.
    • Handle: RePEc:hin:jnlmpe:8591115
    DOI: 10.1155/2023/8591115
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    Cited by:

    1. Samuel Ugwu & Pierre Miasnikof & Yuri Lawryshyn, 2023. "Distance Correlation Market Graph: The Case of S&P500 Stocks," Mathematics, MDPI, vol. 11(18), pages 1-13, September.
    2. Vogl, Markus & Kojić, Milena & Mitić, Petar, 2024. "Dynamics of green and conventional bond markets: Evidence from the generalized chaos analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).

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