In this paper we are interested in decomposing a dihypergraph $\mathcal{H} = (V, \mathcal{E})$ into simpler dihypergraphs, that can be handled more efficiently. We study the properties of dihypergraphs that can be hierarchically decomposed into trivial dihypergraphs, \ie vertex hypergraph. The hierarchical decomposition is represented by a full labelled binary tree called $\mathcal{H}$-tree, in the fashion of hierarchical clustering. We present a polynomial time and space algorithm to achieve such a decomposition by producing its corresponding $\mathcal{H}$-tree. However, there are dihypergraphs that cannot be completely decomposed into trivial components. Therefore, we relax this requirement to more indecomposable dihypergraphs called H-factors, and discuss applications of this decomposition to closure systems and lattices.

中文翻译：

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双超图的层次分解

在本文中，我们感兴趣的是将双超图 $\mathcal{H} = (V, \mathcal{E})$ 分解为可以更有效处理的更简单的双超图。我们研究了可以分层分解为平凡双超图（即顶点超图）的双超图的属性。层次分解由称为 $\mathcal{H}$-tree 的完整标记二叉树表示，采用层次聚类的方式。我们提出了一种多项式时间和空间算法，通过生成其相应的 $\mathcal{H}$-tree 来实现这种分解。但是，有些双超图不能完全分解为琐碎的组件。因此，我们将这个要求放宽到称为 H 因子的更不可分解的二超图，并讨论这种分解在闭合系统和格子中的应用。