Abstract

It is shown that a minimum weight spanning tree of a finite ultrametric space can be always found in the form of path. As a canonical representing tree such path uniquely defines the whole space and, moreover, it has much more simple structure. Thus, minimum spanning paths are a convenient tool for studying finite ultrametric spaces. To demonstrate this we use them for characterization of some known classes of ultrametric spaces. The explicit formula for Hausdorff distance in finite ultrametric spaces is also found. Moreover, the possibility of using minimum spanning paths for finding this distance is shown.

中文翻译：

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有限超度量空间中的最小跨越路径和豪斯多夫距离

摘要

证明了有限超度量空间的最小权重生成树总能以路径的形式找到。作为一个典型的表示树，这样的路径唯一地定义了整个空间，而且，它的结构更加简单。因此，最小跨越路径是研究有限超度量空间的便捷工具。为了证明这一点，我们使用它们来表征一些已知类别的超度量空间。还找到了有限超度量空间中豪斯多夫距离的显式公式。此外，还显示了使用最小跨越路径来找到该距离的可能性。