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：本文致力于枚举所有频繁的最大/闭树问题，这是数据挖掘领域一个经典且核心的课题。尽管针对该问题已发展出许多实用算法，但在树高度满足“现实假设”条件下的计算复杂性尚未得到明确阐释。具体而言，虽然已知当树高度不小于60时挖掘问题将变得困难，但对于树高度更小情况下的复杂性迄今仍未澄清。我们通过建立有序树与无序树、最大与闭树变体等多种设定下这些树挖掘问题的结果，填补了这一研究空白。