An experimental comparison of four graph drawing algorithms
Computational Geometry: Theory and Applications
A better approximation algorithm for finding planar subgraphs
Journal of Algorithms
Software—Practice & Experience - Special issue on discrete algorithm engineering
A Linear Algorithm for the Maximal Planar Subgraph Problem
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Which Aesthetic has the Greatest Effect on Human Understanding?
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
GD'05 Proceedings of the 13th international conference on Graph Drawing
Non-planar core reduction of graphs
GD'05 Proceedings of the 13th international conference on Graph Drawing
A linear time algorithm for finding a maximal planar subgraph based on PC-trees
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
A branch-and-cut approach to the crossing number problem
Discrete Optimization
A note on computing a maximal planar subgraph using PQ-trees
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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The crossing number of a graph G is the smallest number of edge crossings in any drawing of G into the plane. Recently, the first branch-and-cut approach for solving the crossing number problem has been presented in Buchheim et al. [2005]. Its major drawback was the huge number of variables out of which only very few were actually used in the optimal solution. This restricted the algorithm to rather small graphs with low crossing number. In this article, we discuss two column generation schemes; the first is based on traditional algebraic pricing, and the second uses combinatorial arguments to decide whether and which variables need to be added. The main focus of this article is the experimental comparison between the original approach and these two schemes. In addition, we evaluate the quality achieved by the best-known crossing number heuristic by comparing the new results with the results of the heuristic.