Column-Based Graph Layouts

We consider orthogonal upward drawings of directed acyclic graphs with nodes of uniform width but node-specific height. One way to draw such graphs is to use a layering technique as provided by the Sugiyama framework [34]. To overcome one of the drawbacks of the Sugiyama Framework, namely, unnecessary edge crossings caused by an unfortunate layer assignment of the nodes, Chimani et al. integrated their layer-free upward crossing minimization algorithm [9] into the Sugiyama framework [10]. However, one drawback of the Sugiyama framework still remains. If the heights of the nodes are non-uniform, the result of the approach can be a non-compact layout. In contrast, we avoid both of these drawbacks by integrating layer-free upward crossing minimization into the topology-shape-metrics (TSM) framework introduced by Tamassia [35]. Our approach, in combination with an algorithm by Biedl and Kant [4] lets us generate column-based layouts, i. e., layouts where the plane is divided into uniform-width columns and every node is assigned to a column. We study the complexity of the individual steps of the layout process systematically and propose efficient algorithms with provable guarantees. We show that our column-based approach allows to generate visually appealing, compact layouts with few edge crossing and at most four bends per edge. Furthermore, the resulting layouts exhibit a high degree of symmetry and implicitly support edge bundling. We evaluate our approach by applying it to several real-world examples. Submitted: August 2013 Reviewed: November 2013 Revised: January 2014 Reviewed: April 2014 Revised: August 2014 Accepted: December 2014 Final: December 2014 Published: December 2014 Article type: Regular paper Communicated by: S.-H. Hong Preliminary results presented in this paper have appeared as “G. Betz, C. Doll, A. Gemsa, I. Rutter, and D. Wagner, “Column-Based Graph Layouts”, Proceedings of the 20th International Symposium on Graph Drawing (GD’12) , vol. 7704 of LNCS, pp. 236–247, Springer, 2013 [3]. E-mail addresses: [email protected] (Gregor Betz) [email protected] (Andreas Gemsa) (Christof Mathies) [email protected] (Ignaz Rutter) [email protected] (Dorothea