Dynamic variable ordering for ordered binary decision diagrams
ICCAD '93 Proceedings of the 1993 IEEE/ACM international conference on Computer-aided design
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Which Aesthetic has the Greatest Effect on Human Understanding?
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
A Polyhedral Approach to the Multi-Layer Crossing Minimization Problem
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
Communicating Centrality in Policy Network Drawings
IEEE Transactions on Visualization and Computer Graphics
An Improved Bound on the One-Sided Minimum Crossing Number in Two-Layered Drawings
Discrete & Computational Geometry
A Radial Adaptation of the Sugiyama Framework for Visualizing Hierarchical Information
IEEE Transactions on Visualization and Computer Graphics
An approximation algorithm for the two-layered graph drawing problem
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Multi-circular layout of micro/macro graphs
GD'07 Proceedings of the 15th international conference on Graph drawing
Approximating crossing minimization in radial layouts
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Crossing reduction in circular layouts
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
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The most popular method of drawing directed graphs is to place vertices on a set of horizontal or concentric levels, known as level drawings. Level drawings are well studied in Graph Drawing due to their strong application for the visualization of hierarchy in graphs. There are two drawing conventions: Horizontal drawings use a set of parallel lines and radial drawings use a set of concentric circles. In level drawings, edges are only allowed between vertices on different levels. However, many real world graphs exhibit hierarchies with edges between vertices on the same level. In this paper, we initiate the new problem of extended level drawings of graphs, which was addressed as one of the open problems in social network visualization, in particular, displaying centrality values of actors. More specifically, we study minimizing the number of edge crossings in extended level drawings of graphs. The main problem can be formulated as the extended one-sided crossing minimization problem between two adjacent levels, as it is folklore with the one-sided crossing minimization problem in horizontal drawings. We first show that the extended one-sided crossing minimization problem is NP-hard for both horizontal and radial drawings, and then present efficient heuristics for minimizing edge crossings in extended level drawings. Our extensive experimental results show that our new methods reduce up to 30% of edge crossings.