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A heuristic method for solving the Steiner tree problem in graphs using network centralities

Author

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  • Misa Fujita
  • Yutaka Shimada
  • Takayuki Kimura
  • Tohru Ikeguchi

Abstract

We propose a heuristic method of using network centralities for constructing small-weight Steiner trees in this paper. The Steiner tree problem in graphs is one of the practical NP-hard combinatorial optimization problems. Given a graph and a set of vertices called terminals in the graph, the objective of the Steiner tree problem in graphs is to find a minimum weight Steiner tree that is a tree containing all the terminals. Conventional construction methods make a Steiner tree based on the shortest paths between terminals. If these shortest paths are overlapped as much as possible, we can obtain a small-weight Steiner tree. Therefore, we proposed to use network centralities to distinguish which edges should be included to make a small-weight Steiner tree. Experimental results revealed that using the vertex or the edge betweenness centralities contributes to making small-weight Steiner trees.

Suggested Citation

  • Misa Fujita & Yutaka Shimada & Takayuki Kimura & Tohru Ikeguchi, 2024. "A heuristic method for solving the Steiner tree problem in graphs using network centralities," PLOS ONE, Public Library of Science, vol. 19(6), pages 1-16, June.
    • Handle: RePEc:plo:pone00:0303764
    DOI: 10.1371/journal.pone.0303764
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