DAGmaps and ε-visibility representations of DAGs

Authors:
Vassilis Tsiaras;Ioannis G. Tollis
Affiliations:
Institute of Computer Science, Foundation for Research and Technology-Hellas, Department of Computer Science, University of Crete, Heraklion, Greece;Institute of Computer Science, Foundation for Research and Technology-Hellas, Department of Computer Science, University of Crete, Heraklion, Greece
Venue:
GD'09 Proceedings of the 17th international conference on Graph Drawing
Year:
2009

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Abstract

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 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 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.