论文标题
二脑层的分层分解
Hierarchical Decompositions of dihypergraphs
论文作者
论文摘要
在本文中，我们有兴趣将Dihypergraph $ \ MATHCAL {H} =（V，V，\ Mathcal {e}）$分解为更简单的二型二氢巨头，可以更有效地处理。我们研究了可以分层分解为微不足道的二氢图，\ ie顶点超图的二氢图的特性。层次分解由完整标记的二进制树表示，称为$ \ Mathcal {H} $ - 树，以分层聚类的方式表示。我们提出了一个多项式时间和空间算法，通过产生其相应的$ \ Mathcal {H} $ -TREET来实现这种分解。但是，有一些无法将其完全分解成琐碎的成分。因此，我们放宽了这一要求，对称为H-因子的更本不可分解的二氢图，并讨论了这种分解在封闭系统和晶格中的应用。
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.
