We establish bi-Lipschitz bounds certifying quasi-universality (universality up to a constant factor) for various distances between Reeb graphs: the interleaving distance, the functional distortion distance, and the functional contortion distance. The definition of the latter distance is a novel contribution, and for the special case of contour trees we also prove strict universality of this distance. Furthermore, we prove that for the special case of merge trees the functional contortion distance coincides with the interleaving distance, yielding universality of all four distances in this case.

翻译：我们为Reeb 图形之间的不同距离建立了双利普施茨界限,以证明准普遍性(普遍程度至一个不变系数):间断距离、功能扭曲距离和功能调和距离。 后一种距离的定义是一种新的贡献,对于等距树的特殊情况,我们也证明了这种距离的严格普遍性。 此外,我们证明,对于合并树木这一特殊情形,功能调和距离与相互交错距离相吻合,从而使得所有四个距离都具有普遍性。