Optimal Upward Planarity Testing of Single-Source Digraphs
SIAM Journal on Computing
An experimental comparison of four graph drawing algorithms
Computational Geometry: Theory and Applications
On the Computational Complexity of Upward and Rectilinear Planarity Testing
SIAM Journal on Computing
GD'07 Proceedings of the 15th international conference on Graph drawing
Mixed upward planarization – fast and robust
GD'05 Proceedings of the 13th international conference on Graph Drawing
An efficient implementation of sugiyama's algorithm for layered graph drawing
GD'04 Proceedings of the 12th international conference on Graph Drawing
Crossing minimization and layouts of directed hypergraphs with port constraints
GD'10 Proceedings of the 18th international conference on Graph drawing
An SDP approach to multi-level crossing minimization
Journal of Experimental Algorithmics (JEA)
Grid sifting: Leveling and crossing reduction
Journal of Experimental Algorithmics (JEA)
GD'12 Proceedings of the 20th international conference on Graph Drawing
Upward planarity testing via SAT
GD'12 Proceedings of the 20th international conference on Graph Drawing
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An upward drawing of a DAG G is a drawing of G in which all arcs are drawn as curves increasing monotonically in the vertical direction. In this article, we present a new approach for upward crossing minimization, that is, 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 reinserts the remaining arcs 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.