六针肥皂膜中的Steiner树和生成树
Steiner trees and spanning trees in six-pin soap films
摘要：
我们已经研究了Steiner树问题，使用六针肥皂膜详细。我们扩展现有的方法，实验实现Steiner树的$n$终端问题，通过肥皂膜观察新的非最小Steiner树。我们还产生了生成树配置的第一次，我们的方法。实验上，通过改变针的直径，我们已经实现了这些新的稳定的肥皂膜配置。从理论上提出了一种新的生成Steiner树的算法。这些斯坦纳树配置的精确长度使用几何方法计算。提出了一个精确的双参数经验公式来估计六针肥皂膜问题中这些肥皂膜结构的长度。
英文摘要：
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.
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