REU Project
- On Steiner Trees of the Regular Simplex
- Project Year: 2023
- REU Student (s): Guillermo Gamboa | Charles University (Prague, Czech Republic) | Josef Matejka | Charles University (Prague, Czech Republic) | Jakub Petr | Charles University (Prague, Czech Republic)
- Project Mentor (s) : Karthik Srikanta - Computer Science
- Project Abstract:
In this project, we studied Steiner minimal trees for the points given by the corners of the regular simplex. We provide an explicit formula for the coordinates of the Steiner points of a conjectured Steiner minimal tree for simplexes of dimension 2k-1. Also, we explore the function APTC(T), a notion used to characterize trees with respect to the sum of all distances between the terminals, and proved that the conjectured topology for Steiner minimal trees for the regular simplex minimizes this function over all tree with n terminals and n-2 interior points.