Steiner Tree Heuristic in the Euclidean d-Space Using Bottleneck Distances

Abstract

Some of the most efficient heuristics for the Euclidean Steiner minimal trees in the d-dimensional space, d ≥ 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 low cost trees spanning all terminals. The weakness of this approach is that obtained solutions are topologically related to minimum spanning trees. To obtain 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.

A new second‐order conic optimization model for the Euclidean Steiner tree problem in Rd$\mathbb {R}^d$

“…Finally, for more recent heuristic approaches, one can refer to Do Forte et al. (2015), Lorenzen and Winter (2016), Whittle et al. (2020), Pinto and Maculan (2022), Montenegro et al (2002), and the references therein.…”