We define and study a new structural parameter for directed graphs, which we call \emph{ear anonymity}. Our parameter aims to generalize the useful properties of \emph{funnels} to larger digraph classes. In particular, funnels are exactly the acyclic digraphs with ear anonymity one. We prove that computing the ear anonymity of a digraph is \NP/-hard and that it can be solved in $O(m(n + m))$-time on acyclic digraphs (where \(n\) is the number of vertices and \(m\) is the number of arcs in the input digraph). It remains open where exactly in the polynomial hierarchy the problem of computing ear anonymity lies, however for a related problem we manage to show $\Sigma_2^p$-completeness.

翻译：我们定义并研究了一种新的有向图结构参数，称为耳匿名性。该参数旨在将漏斗的有用属性推广到更大的有向图类中。具体而言，漏斗恰好是耳匿名性为1的无环有向图。我们证明，计算有向图的耳匿名性是NP难的，并且可以在$O(m(n + m))$时间内解决无环有向图上的问题（其中$n$是输入有向图中的顶点数，$m$是弧数）。关于计算耳匿名性问题在多项式层次中的确切位置，目前仍是一个开放问题，然而对于相关问题，我们成功证明其是$\Sigma_2^p$完全的。