Reverse search is a convenient method for enumerating structured objects, that can be used both to address theoretical issues and to solve data mining problems. This method has already been successfully developed to handle unordered trees. If the literature proposes solutions to enumerate singletons of trees, we study in this article a more general, higher combinatorial problem, the enumeration of sets of trees - forests. By compressing each forest into a Directed Acyclic Graph (DAG), we develop a reverse search like method to enumerate DAG compressing forests. Remarkably, we prove that these DAG are in bijection with the row-Fishburn matrices, a well-studied class of combinatorial objects. In a second step, we derive our forest enumeration to provide algorithms for tackling two related problems : (i) the enumeration of "subforests" of a forest, and (ii) the frequent "subforest" mining problem. All the methods presented in this article enumerate each item uniquely, up to isomorphism.

中文翻译：

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无序森林的枚举

反向搜索是一种枚举结构化对象的便捷方法，可用于解决理论问题和解决数据挖掘问题。这种方法已经被成功开发用于处理无序树。如果文献提出了枚举单例树的解决方案，我们将在本文中研究一个更一般、更高的组合问题，即树集的枚举 - 森林。通过将每个森林压缩成有向无环图 (DAG)，我们开发了一种类似反向搜索的方法来枚举 DAG 压缩森林。值得注意的是，我们证明了这些 DAG 与 row-Fishburn 矩阵双射，这是一种经过充分研究的组合对象类。第二步，我们推导出我们的森林枚举，以提供解决两个相关问题的算法：（i）“子森林”的枚举 森林，以及 (ii) 频繁出现的“亚森林”采矿问题。本文中介绍的所有方法都唯一地枚举了每个项目，直至同构。