Week 3. Steiner Trees of Regular Simplices

During this week, we realized that our planned reduction from Vertex Cover to the approximate Euclidean Steiner tree problem in $\mathbb{R}^n$ requires showing that configurations of points in a regular simplex form the lowest weight Steiner trees in a particular setting.

Using Sage, nauty, and Smith's exact Steiner tree algorithm, we tested whether this is the case for configurations arising from graphs of low size. Our conjectures align with the computational evidence. However, as of yet, we are unable to prove that simplices are the best in this particular setting.