DAGmaps and ε-Visibility Representations of DAGs
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.
KeywordsDAGmap Treemap DAG Visibility
- 3.Bruls, M., Huizing, K., van Wijk, J.: Squarified treemaps. In: de Leeuw, W., van Liere, R. (eds.) Data Visualization 2000, Proceedings of the Second Joint Eurographics and IEEE TCVG Symposium on Visualization, pp. 33–42 (2000)Google Scholar
- 4.Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall, Upper Saddle River (1998)Google Scholar
- 8.Lü, H., Fogarty, J.: Cascaded treemaps: examining the visibility and stability of structure in treemaps. In: ACM Proceedings of graphics interface 2008, pp. 259–266 (2008)Google Scholar
- 9.Romanik, K.: Directed VR-representable graphs have unbounded dimension. In: Tamassia, R., Tollis, I.G. (eds.) GD 1994. LNCS, vol. 894, pp. 177–181. Springer, Heidelberg (1995)Google Scholar
- 12.Tsiaras, V.: Algorithms for the Analysis and Visualization of Biomedical Networks. Ph.D. thesis, Computer Science Department, University of Crete (2009) (submitted)Google Scholar