In this paper, we address the problem of enumerating all frequent maximal/closed trees. This is a classical and central problem in data mining. Although many practical algorithms have been developed for this problem, its complexity under ``realistic assumptions'' on tree height has not been clarified. More specifically, while it was known that the mining problem becomes hard when the tree height is at least 60, the complexity for cases where the tree height is smaller has not yet been clarified. We resolve this gap by establishing results for these tree mining problems under several settings, including ordered and unordered trees, as well as maximal and closed variants.

翻译：本文探讨了枚举所有频繁最大/闭合树的问题，这是数据挖掘中的一个经典核心问题。尽管针对该问题已开发出许多实用算法，但关于树高度在"现实假设"下的复杂性尚未明确。具体而言，虽然已知当树高度至少为60时挖掘问题会变得困难，但对于树高度较小的情况其复杂性仍未得到澄清。我们通过建立有序树与无序树、最大与闭合变体等多种设置下的树挖掘问题结果，填补了这一研究空白。