English

Some minimum networks for four points in the three dimensional Euclidean Space

Metric Geometry 2020-01-22 v1 Optimization and Control

Abstract

We construct a minimum tree for some boundary symmetric tetrahedra R^3, which has two nodes (interior points) with equal weights (positive numbers) having the property that the common perpendicular of some two opposite edges passes through their midpoints. We prove that the length of this minimum tree may have length less than the length of the full Steiner tree for the same boundary symmetric tetrahedra.

Keywords

Cite

@article{arxiv.2001.06866,
  title  = {Some minimum networks for four points in the three dimensional Euclidean Space},
  author = {Anastasios Zachos},
  journal= {arXiv preprint arXiv:2001.06866},
  year   = {2020}
}

Comments

9 pages, 2 figures

R2 v1 2026-06-23T13:15:06.208Z