Journal Article10.1145/1671970.1671975
Layer-free upward crossing minimization
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TL;DR: This article presents a new approach for upward crossing minimization, that is, finding an upward drawing of a DAG G with as few crossings as possible, based on a two-stage upward planarization approach, which computes a feasible downward planar subgraph in the first step and reinserts the remaining arcs by computing constraint-feasible upward insertion paths.
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Abstract: 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.
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Citations
The Graph Crossing Number and its Variants: A Survey
TL;DR: A survey of the rich variety of crossing number variants that have been introduced in the literature for purposes that range from studying the theoretical underpinnings of the crossing number to crossing minimization for visualization problems.
203
•Proceedings Article
The Open Graph Drawing Framework (OGDF)
Markus Chimani,Carsten Gutwenger,Michael Jünger,Gunnar W. Klau,Karsten Klein,Petra Mutzel +5 more
- 01 Jan 2012
TL;DR: Cluster Layout Planarity testing Booth/Lueker and Boyer/Myrvold Cluster (Feng et al.), Upward (Bertolazzi et al.) Customizable planarization method Edge insertion (fixed & variable embedding) Crossing.
198
•Proceedings Article
Hierarchical Drawing Algorithms.
Patrick Healy,Nikola S. Nikolov +1 more
- 01 Jan 2013
TL;DR: The University of Limerick 17.17.2018, Limerick, Ireland as discussed by the authors, Dublin, Ireland, United Kingdom, Ireland.Reference as discussed by the authors : http://www.universityof-limerick.edu.
72
The Open Graph Drawing Framework
Markus Chimani,Carsten Gutwenger,Michael Jünger,Gunnar W. Klau,Karsten Klein,Petra Mutzel +5 more
- 01 Jan 2013
TL;DR: The goals for the Open Graph Drawing Framework (OGDF) were to transfer essential design concepts of AGD and to overcome its main deficiencies for use in academic research.
49
•Proceedings Article
An SDP approach to multi-level crossing minimization
Markus Chimani,Philipp Hungerländer,Michael Jünger,Petra Mutzel +3 more
- 22 Jan 2011
TL;DR: In this paper, a semidefinite program (SDP) based approach was proposed to solve the multi-level crossing minimization problem, in which the graph's vertices are assigned to multiple parallel levels and the problem of ordering the nodes on their levels such that, when drawing the graph with straight lines, the resulting number of crossings is minimized.
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