A heuristic method for solving the Steiner tree problem in graphs using network centralities
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Updated: Jun 24, 2025

Modeling the Functional Network for Spatial Navigation in the Human Brain
Published on: October 13, 2023
Misa Fujita1,2, Yutaka Shimada3, Takayuki Kimura4
1Department of Electrical and Electronic Engineering, School of Engineering, Chukyo University, Nagoya-shi, Aichi, Japan.
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.
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