We consider the setting of Reeb graphs of piecewise linear functions and study distances between them that are stable, meaning that functions which are similar in the supremum norm ought to have similar Reeb graphs. We define an edit distance for Reeb graphs and prove that it is stable and universal, meaning that it provides an upper bound to any other stable distance. In contrast, via a specific construction, we show that the interleaving distance and the functional distortion distance on Reeb graphs are not universal.

中文翻译：

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锐步图编辑距离是通用的

我们考虑设置分段线性函数的Reeb图，并研究它们之间的稳定距离，这意味着在最高范数中相似的函数应该具有相似的Reeb图。我们为Reeb图定义了一个编辑距离，并证明它是稳定且通用的，这意味着它为任何其他稳定距离提供了上限。相比之下，通过特定的构造，我们表明Reeb图上的交织距离和功能失真距离不是通用的。