Layer-Free Upward Crossing Minimization
An upward drawing of a DAG G is a drawing of G in which all edges are drawn as curves increasing monotonically in the vertical direction. In this paper, we present a new approach for upward crossing minimization, i.e., finding an upward drawing of a DAG G with as few crossings as possible. Our algorithm is based on a two-stage upward planarization approach, which computes a feasible upward planar subgraph in the first step, and re-inserts the remaining edges by computing constraint-feasible upward insertion paths. An experimental study shows that the new algorithm leads to much better results than existing algorithms for upward crossing minimization, including the classical Sugiyama approach.
KeywordsShort Path Directed Acyclic Graph Insertion Sequence Constraint Feasibility Internal Face
Unable to display preview. Download preview PDF.
- 7.Eiglsperger, M., Siebenhaller, M., Kaufmann, M.: An efficient implementation of Sugiyama’s algorithm for layered graph drawing. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 155–166. Springer, Heidelberg (2005)Google Scholar
- 8.Gansner, E., Koutsofios, E., North, S., Vo, K.-P.: A technique for drawing directed graphs. Software Pract. Exper. 19(3), 214–229 (1993)Google Scholar
- 10.Gutwenger, C., Mutzel, P.: An experimental study of crossing minimization heuristics. In: Liotta, G. (ed.) GD 2003. LNCS, vol. 2912, pp. 13–24. Springer, Heidelberg (2004)Google Scholar
- 11.OGDF – the Open Graph Drawing Framework. Technical University of Dortmund, Chair of Algorithm Engineering, http://www.ogdf.net