Non-planar core reduction of graphs

Authors:
Carsten Gutwenger;Markus Chimani
Affiliations:
University of Dortmund, Dortmund, Germany;University of Dortmund, Dortmund, Germany
Venue:
GD'05 Proceedings of the 13th international conference on Graph Drawing
Year:
2005

Citing 4
Cited 4

On-Line Planarity Testing

SIAM Journal on Computing
An experimental comparison of four graph drawing algorithms

Computational Geometry: Theory and Applications
Efficient Planarity Testing

Journal of the ACM (JACM)
A Linear Time Implementation of SPQR-Trees

GD '00 Proceedings of the 8th International Symposium on Graph Drawing

A New Approach to Exact Crossing Minimization

ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Experiments on exact crossing minimization using column generation

Journal of Experimental Algorithmics (JEA)
Experiments on exact crossing minimization using column generation

WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
A branch-and-cut approach to the crossing number problem

Discrete Optimization

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Abstract

We present a reduction method that reduces a graph to a smaller core graph which behaves invariant with respect to planarity measures like crossing number, skewness, and thickness. The core reduction is based on the decomposition of a graph into its triconnected components and can be computed in linear time. It has applications in heuristic and exact optimization algorithms for the planarity measures mentioned above. Experimental results show that this strategy yields a reduction to 2/3 in average for a widely used benchmark set of graphs.