Construction of a Steiner Tree Using the Clustering Method

Abstract

This paper examines the method of constructing a Steiner tree for optimizing network structures in distributed computer systems. The primary goal of the work is to investigate and implement an advanced algorithm for finding Steiner points using the clustering method. The main idea of the method is to use a specific approach to determining Steiner points that opti-mize the connection of given points in space. The objective of this approach is to reduce com-putational complexity while maintaining adequate accuracy in constructing the Steiner tree. Due to the simplified approach to clustering and determining Steiner points, this method has the potential to significantly optimize the problem-solving process, especially in scenarios with a large number of points. To determine its effectiveness, studies were conducted on graphs with four, five, and six vertices randomly located on a plane. Testing was carried out using special software written in Python. Overall, the research showed that the clustering method is an effective tool for determining Steiner points, allowing for reduced computational complexity and providing adequate accuracy in constructing the Steiner tree. Further re-search in this direction may contribute to the improvement of network structure optimization methods, which is important for a wide range of practical applications.