A new perspective on clustered planarity as a combinatorial embedding problem

The clustered planarity problem (c-planarity) asks whether a hierarchically clustered graph admits a planar drawing such that the clusters can be nicely represented by regions. We introduce the cd-tree data structure and give a new characterization of c-planarity. It leads to efficient algorithms fo...

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Bibliographic Details
Published inTheoretical computer science Vol. 609; pp. 306 - 315
Main Authors Bläsius, Thomas, Rutter, Ignaz
Format Journal Article
LanguageEnglish
Published Elsevier B.V 04.01.2016
Subjects
Algorithms
Cadmium
Characterization
Clustered planarity
Clusters
Combinatorial analysis
Complement
Constrained planar embedding
Graph drawing
Graph theory
Joints
Characterization
Graph drawing
Algorithms
Clustered planarity
Constrained planar embedding
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Summary:The clustered planarity problem (c-planarity) asks whether a hierarchically clustered graph admits a planar drawing such that the clusters can be nicely represented by regions. We introduce the cd-tree data structure and give a new characterization of c-planarity. It leads to efficient algorithms for c-planarity testing in the following cases. (i) Every cluster and every co-cluster (complement of a cluster) has at most two connected components. (ii) Every cluster has at most five outgoing edges. Moreover, the cd-tree reveals interesting connections between c-planarity and planarity with constraints on the order of edges around vertices. On one hand, this gives rise to a bunch of new open problems related to c-planarity, on the other hand it provides a new perspective on previous results.
Bibliography:ObjectType-Article-1
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2015.10.011