An experimental comparison of four graph drawing algorithms
Computational Geometry: Theory and Applications
Software—Practice & Experience - Special issue on discrete algorithm engineering
Planarization of Clustered Graphs
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
Advances in C-Planarity Testing of Clustered Graphs
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Planarity for Clustered Graphs
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
A Linear Time Algorithm to Recognize Clustered Graphs and Its Parallelization
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
Efficient extraction of multiple kuratowski subdivisions
GD'07 Proceedings of the 15th international conference on Graph drawing
Efficient C-planarity testing for embedded flat clustered graphs with small faces
GD'07 Proceedings of the 15th international conference on Graph drawing
Clustered planarity: small clusters in Eulerian graphs
GD'07 Proceedings of the 15th international conference on Graph drawing
C-planarity of extrovert clustered graphs
GD'05 Proceedings of the 13th international conference on Graph Drawing
Clustering cycles into cycles of clusters
GD'04 Proceedings of the 12th international conference on Graph Drawing
Shrinking the search space for clustered planarity
GD'12 Proceedings of the 20th international conference on Graph Drawing
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Deciding c-planarity for a given clustered graph C = (G ,T ) is one of the most challenging problems in current graph drawing research. Though it is yet unknown if this problem is solvable in polynomial time, latest research focused on algorithmic approaches for special classes of clustered graphs. In this paper, we introduce an approach to solve the general problem using integer linear programming (ILP) techniques. We give an ILP formulation that also includes the natural generalization of c-planarity testing--the maximum c-planar subgraph problem --and solve this ILP with a branch-and-cut algorithm. Our computational results show that this approach is already successful for many clustered graphs of small to medium sizes and thus can be the foundation of a practically efficient algorithm that integrates further sophisticated ILP techniques.