Some Analytics for Steiner Minimal Tree Problem for Four Terminals

TL;DR

This paper derives explicit formulas for the Steiner points in the minimal tree connecting four terminals in the Euclidean plane, enabling analysis of how terminal positions affect Steiner point locations.

Contribution

It provides the first explicit formulas for Steiner point coordinates in the four-terminal Euclidean Steiner minimal tree problem.

Findings

Formulas for Steiner point coordinates are explicitly derived.

Terminal positions influence Steiner point locations significantly.

The formulas facilitate analysis of Steiner tree configurations.

Abstract

Given the coordinates of four terminals in the Euclidean plane we present explicit formulas for Steiner point coordinates for Steiner minimal tree problem. We utilize the obtained formulas for evaluation of the influence of terminal coordinates on the loci of Steiner points.