DAGmaps are space filling visualizations of DAGs that generalize treemaps. Deciding whether or not a DAG admits a DAGmap is NP-complete. Recently we defined a special case called one-dimensional DAGmap where the admissibility is decided in linear time. However there is no complete characterization of the class of DAGs that admit a onedimensional DAGmap. In this paper we prove that a DAG admits a one-dimensional DAGmap if and only if it admits a directed ε-visibility representation. Then we give a characterization of the DAGs that admit directed ε-visibility representations. Finally we show that a DAGmap defines a directed three-dimensional ε-visibility representation of a DAG. Keywords: DAGmap, Treemap, DAG, Visibility.\ud\ud
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机译：DAGmap是DAG的空间填充可视化，用于概括树图。确定DAG是否接受DAGmap是NP完整的。最近，我们定义了一种称为一维DAGmap的特殊情况，其中可允许性是在线性时间中确定的。但是，并没有完全承认一维DAGmap的DAG类的特征。在本文中，我们证明，当且仅当DAG接受定向ε可见性表示时，它才接受一维DAG映射。然后，我们给出DAG的特征，这些DAG可以接受有向的ε-可见性表示。最后，我们表明DAGmap定义了DAG的定向三维ε-可见性表示。关键字：DAGmap，树形图，DAG，可见性。\ ud \ ud
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