SIAM Journal on Computing
Journal of the ACM (JACM)
Straight-Line Drawing Algorithms for Hierarchical Graphs and Clustered Graphs
GD '96 Proceedings of the Symposium on Graph Drawing
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
Multilevel Visualization of Clustered Graphs
GD '96 Proceedings of the Symposium on Graph Drawing
A Linear Time Algorithm to Recognize Clustered Graphs and Its Parallelization
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
PC trees and circular-ones arrangements
Theoretical Computer Science - Computing and combinatorics
Journal of Computer and System Sciences
Clustering cycles into cycles of clusters
GD'04 Proceedings of the 12th international conference on Graph Drawing
Clustered Planarity: Clusters with Few Outgoing Edges
Graph Drawing
Computing Maximum C-Planar Subgraphs
Graph Drawing
Straight-Line Rectangular Drawings of Clustered Graphs
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Efficient C-planarity testing for embedded flat clustered graphs with small faces
GD'07 Proceedings of the 15th international conference on Graph drawing
Splitting clusters to get c-planarity
GD'09 Proceedings of the 17th 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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A clustered graph has its vertices grouped into clusters in a hierarchical way via subset inclusion, thereby imposing a tree structure on the clustering relationship. The c-planarity problem is to determine if such a graph can be drawn in a planar way, with clusters drawn as nested regions and with each edge (drawn as a curve between vertex points) crossing the boundary of each region at most once. Unfortunately, as with the graph isomorphism problem, it is open as to whether the c-planarity problem is NP-complete or in P. In this paper, we show how to solve the c-planarity problem in polynomial time for a new class of clustered graphs, which we call extrovert clustered graphs. This class is quite natural (we argue that it captures many clustering relationships that are likely to arise in practice) and includes the clustered graphs tested in previous work by Dahlhaus, as well as Feng, Eades, and Cohen. Interestingly, this class of graphs does not include, nor is it included by, a class studied recently by Gutwenger et al.; therefore, this paper offers an alternative advancement in our understanding of the efficient drawability of clustered graphs in a planar way. Our testing algorithm runs in O(n3) time and implies an embedding algorithm with the same time complexity.