Area, Curve Complexity, and Crossing Resolution of Non-Planar Graph Drawings

In this paper we study non-planar drawings of graphs, and study trade-offs between the crossing resolution (i.e., the minimum angle formed by two crossing segments), the curve complexity (i.e., maximum number of bends per edge), the total number of bends, and the area.

[1]  Helen C. Purchase,et al.  Effective information visualisation: a study of graph drawing aesthetics and algorithms , 2000, Interact. Comput..

[2]  Walter Didimo,et al.  Drawing graphs with right angle crossings , 2009, Theor. Comput. Sci..

[3]  Michael Kaufmann,et al.  On the Perspectives Opened by Right Angle Crossing Drawings , 2009, J. Graph Algorithms Appl..

[4]  G. Szekeres,et al.  A combinatorial problem in geometry , 2009 .

[5]  David A. Carrington,et al.  Empirical Evaluation of Aesthetics-based Graph Layout , 2002, Empirical Software Engineering.

[6]  Weidong Huang.  An Eye Tracking Study into the Effects of Graph Layout , 2008, ArXiv.

[7]  Joachim Gudmundsson,et al.  Notes on Large Angle Crossing Graphs , 2009, Chic. J. Theor. Comput. Sci..

[8]  Géza Tóth,et al.  Note on the Erdos - Szekeres Theorem , 1998, Discret. Comput. Geom..

[9]  Weidong Huang,et al.  Using eye tracking to investigate graph layout effects , 2007, 2007 6th International Asia-Pacific Symposium on Visualization.

[10]  Csaba D. Tóth,et al.  Graphs that Admit Right Angle Crossing Drawings , 2010, WG.

[11]  David R. Wood,et al.  Grid drawings of k-colourable graphs , 2005, Comput. Geom..

[12]  Michael Jünger,et al.  Graph Drawing Software , 2003, Graph Drawing Software.

[13]  Peter Eades,et al.  Effects of Crossing Angles , 2008, 2008 IEEE Pacific Visualization Symposium.

[14]  Ioannis G. Tollis,et al.  Efficient Orthogonal Drawings of High Degree Graphs , 2000, Algorithmica.

[15]  R. Fulek,et al.  Drawing Graphs with Orthogonal Crossings , 2010, 1001.3117.

[16]  Emilio Di Giacomo,et al.  Area, Curve Complexity, and Crossing Resolution of Non-Planar Graph Drawings , 2009, Theory of Computing Systems.

[17]  Colin Ware,et al.  Cognitive Measurements of Graph Aesthetics , 2002, Inf. Vis..

[18]  Walter Didimo,et al.  A characterization of complete bipartite RAC graphs , 2010, Inf. Process. Lett..