Planarity testing and optimal edge insertion with embedding constraints

Authors:
Carsten Gutwenger;Karsten Klein;Petra Mutzel
Affiliations:
University of Dortmund, Germany;University of Dortmund, Germany;University of Dortmund, Germany
Venue:
GD'06 Proceedings of the 14th international conference on Graph drawing
Year:
2006

Citing 9
Cited 2

Computer aided layout of entity relationship diagrams

Journal of Systems and Software - Special double issue on the entity-relationship approach to databases and related software
A linear algorithm for embedding planar graphs using PQ-trees

Journal of Computer and System Sciences
Using constraints to achieve stability in automatic graph layout algorithms

CHI '90 Proceedings of the SIGCHI Conference on Human Factors in Computing Systems
On-Line Planarity Testing

SIAM Journal on Computing
Efficient Planarity Testing

Journal of the ACM (JACM)
Drawing database schemas

Software—Practice & Experience
Incremental Layout in DynaDAG

GD '95 Proceedings of the Symposium on Graph Drawing
A Bayesian Paradigm for Dynamic Graph Layout

GD '97 Proceedings of the 5th International Symposium on Graph Drawing
Sketch-Driven Orthogonal Graph Drawing

GD '02 Revised Papers from the 10th International Symposium on Graph Drawing

An SPQR-Tree Approach to Decide Special Cases of Simultaneous Embedding with Fixed Edges

Graph Drawing
Practical level planarity testing and layout with embedding constraints

GD'07 Proceedings of the 15th international conference on Graph drawing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Many practical applications demand additional restrictions on an admissible planar embedding. In particular, constraints on the permitted (clockwise) order of the edges around a vertex, like so-called side constraints, abound. In this paper, we introduce a set of hierarchical embedding constraints that also comprises side constraints. We present linear time algorithms for testing if a graph is ec-planar, i.e., admits a planar embedding satisfying the given embedding constraints, as well as for computing such an embedding. Moreover, we characterize the set of all possible ec-planar embeddings and consider the problem of finding a planar combinatorial embedding of a planar graph such that an additional edge can be inserted with the minimum number of crossings; we show that this problem can still be solved in linear time under the additional restrictions of embedding constraints.