DAGmaps and ε-Visibility Representations for DAGs: Algorithms and Characterizations

Abstract

DAGmaps are space filling visualizations of DAGs that generalize treemaps. Deciding whether or not a DAG admits a DAGmap is NP-complete. Although any layered planar DAG admits a one-dimensional DAGmap there was no complete characterization of the class of DAGs that admit a one-dimensional 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 characterize the class of DAGs that admit directed ε-visibility representations. This class consists of the DAGs that admit a downward planar straight-line drawing such that all source and sink vertices are assigned to the external face. Finally we show that a DAGmap defines a directed three-dimensional ε-visibility representation of a DAG.
Key words: Graph Drawing, Visibility Representations, DAGmaps,
Treemaps, Planar st-Graphs