We show in this paper a bijection between totally balanced hypergraphs and so-called totally balanced dissimilarities. We give an efficient way ( O ( n 3 ) where n is the number of elements) to (i) recognize if a given dissimilarity is totally balanced and (ii) approximate it if it is not the case. We also introduce a new kind of dissimilarity which generalizes chordal graphs and allows a polynomial number of clusters that can be easily computed and interpreted.

中文翻译：

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完全平衡的差异

我们在本文中展示了完全平衡的超图和所谓的完全平衡的不同之间的双射。我们给出了一种有效的方法（ O ( n 3 ) 其中 n 是元素的数量）来（i）识别给定的差异是否完全平衡，以及（ii）如果不是这种情况，则对其进行近似。我们还引入了一种新的相异性，它概括了弦图，并允许多项式数量的聚类可以轻松计算和解释。