Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms
Linear Time Planarity Testing and Embedding of Strongly Connected Cyclic Level Graphs
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Gravisto: graph visualization toolkit
GD'04 Proceedings of the 12th international conference on Graph Drawing
Coordinate Assignment for Cyclic Level Graphs
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Drawing directed graphs clockwise
GD'09 Proceedings of the 17th international conference on Graph Drawing
| Hi-index | 0.00 |
The Sugiyama framework is the most commonly used concept for visualizing directed graphs. It draws them in a hierarchical way and operates in four phases: cycle removal, leveling, crossing reduction, and coordinate assignment. However, there are situations where cycles must be displayed as such, e. g., distinguished cycles in the biosciences and processes that repeat in a daily or weekly turn. This forbids the removal of cycles. In their seminal paper Sugiyama et al. also introduced recurrent hierarchies as a concept to draw graphs with cycles. However, this concept has not received much attention since then. In this paper we investigate the leveling problem for cyclic graphs. We show that minimizing the sum of the length of all edges is ${\mathcal{NP}}$-hard for a given number of levels and present three different heuristics for the leveling problem. This sharply contrasts the situation in the hierarchical style of drawing directed graphs, where this problem is solvable in polynomial time.