Planarity Testing and Optimal Edge Insertion with Embedding Constraints

The planarization method has proven to be successful in graph drawing. The output, a combinatorial planar embedding of the so-called planarized graph, can be combined with state-of-the-art planar drawing algorithms. However, many practical applications have additional constraints on the drawings that result in restrictions on the set of admissible planar embeddings. In this paper, we consider embedding constraints that restrict the admissible order of incident edges around a vertex. Such constraints occur in applications, e.g., from side or port constraints. We introduce a set of hierarchical embedding constraints that include grouping, oriented, and mirror constraints, and show how these constraints can be integrated into the planarization method. For this, we first present a linear time algorithm for testing if a given graph G is ec-planar, i.e., admits a planar embedding satisfying the given embedding constraints. In the case that G is ec-planar, we provide a linear time algorithm ...

• Type: Conference
• Year: 2006
• Where: GD
• Authors: Carsten Gutwenger, Karsten Klein, Petra Mutzel
• Keywords: Computer Graphics, Embedding Constraints, GD 2006, Linear Time Algorithm, Planar Embedding