Dynamic variable ordering for ordered binary decision diagrams
ICCAD '93 Proceedings of the 1993 IEEE/ACM international conference on Computer-aided design
A Polyhedral Approach to the Multi-Layer Crossing Minimization Problem
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
Fast and Simple Horizontal Coordinate Assignment
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
A Radial Adaptation of the Sugiyama Framework for Visualizing Hierarchical Information
IEEE Transactions on Visualization and Computer Graphics
Linear Time Planarity Testing and Embedding of Strongly Connected Cyclic Level Graphs
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Crossing reduction in circular layouts
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Journal of Experimental Algorithmics (JEA)
UNTANGLED: A Game Environment for Discovery of Creative Mapping Strategies
ACM Transactions on Reconfigurable Technology and Systems (TRETS)
On the curve complexity of upward planar drawings
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
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Directed graphs are commonly drawn by the Sugiyama algorithm, where crossing reduction is a crucial phase. It is done by repeated one-sided 2-level crossing minimizations, which are still ${\mathcal{NP}}$-hard. We introduce a global crossing reduction, which at any particular time captures all crossings, especially for long edges. Our approach is based on the sifting technique and improves the level-by-level heuristics in the hierarchic framework by a further reduction of the number of crossings by 5 – 10%. In addition it avoids type 2 conflicts which help to straighten the edges, and has a running time which is quadratic in the size of the input graph independently of dummy vertices. Finally, the approach can directly be extended to cyclic, radial, and clustered level graphs where it achieves similar improvements over the previous algorithms.