Minimisation of Networks Based on Computational Geometry Data Structures

Abstract

In this paper, we deal with a problem of finding the shortest interconnection of points given in a Euclidean plane. The traditional strategy starts from the complete graph and finds its minimum spanning tree. However, this approach is proportional to the second power of the number of vertices, and, therefore, not very efficient. Additionally, if, instead of minimum spanning trees, minimum Steiner trees are considered, then the total length of the final network is decreased. Since the Steiner tree problem is NP-hard, in the case of large instances, heuristics must be used. Here, we propose a Delaunay triangulation-based deterministic heuristic and show that it gives very good results in short times.