Hierarchical Decompositions of Dihypergraphs

In this paper we are interested in decomposing a dihypergraph H = (V, E) into simpler dihypergraphs, that can be handled more e ciently. We study the properties of dihypergraphs that can be hierarchically decomposed into trivial dihypergraphs, i.e., vertex hypergraph. The hierarchical decomposition is represented by a full labelled binary trees called 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 H-tree. However , there are dihypergraphs that cannot be completely decomposed into trivial components. Therefore, we relax this requirement to more indecomposable di-hypergraphs called H-factors, and discuss applications of this decomposition to closure systems and lattices.

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