DAGmaps and ε-Visibility Representations of DAGs
Tollis, Ioannis G. and Tsiaras, Vassilis (2010) DAGmaps and ε-Visibility Representations of DAGs. In: Graph Drawing 17th International Symposium, GD 2009, September 22-25, 2009, Chicago, IL, USA , pp. 357-368 (Official URL: http://dx.doi.org/10.1007/978-3-642-11805-0_34).
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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.
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