Steiner trees and spanning trees in six-pin soap films

TL;DR

This paper explores the use of soap films to experimentally realize and analyze Steiner and spanning trees in a six-pin setup, introducing new configurations, a theoretical algorithm, and empirical length estimation formulas.

Contribution

It extends soap film methods to observe new non-minimal Steiner trees and spanning trees, and presents a new algorithm and empirical formulas for their analysis.

Findings

Discovery of new stable soap film Steiner trees

First production of spanning tree configurations with soap films

Development of a new algorithm and empirical length formula

Abstract

We have studied the Steiner tree problem using six-pin soap films in detail. We extend the existing method of experimental realisation of Steiner trees in $n$-terminal problem through soap films to observe new non-minimal Steiner trees. We also produced spanning tree configurations for the first time by our method. Experimentally, by varying the pin diameter, we have achieved these new stable soap film configurations. A new algorithm is presented for creating these Steiner trees theoretically. Exact lengths of these Steiner tree configurations are calculated using a geometrical method. An exact two-parameter empirical formula is proposed for estimating the lengths of these soap film configurations in six-pin soap film problem.