Steiner Tree Heuristic in the Euclidean D-Space Using Bottleneck Distances.

Some of the most efficient heuristics for the Euclidean Steiner minimal tree problem in the d-dimensional space, \(d \ge 2\), use Delaunay tessellations and minimum spanning trees to determine small subsets of geometrically close terminals. Their low-cost Steiner trees are determined and concatenated in a greedy fashion to obtain a low cost tree spanning all terminals. The weakness of this approach is that obtained solutions are topologically related to minimum spanning trees. To avoid this and to obtain even better solutions, bottleneck distances are utilized to determine good subsets of terminals without being constrained by the topologies of minimum spanning trees. Computational experiments show a significant solution quality improvement.