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
String graphs. II.: Recognizing string graphs is NP-hard
Journal of Combinatorial Theory Series B
An experimental comparison of four graph drawing algorithms
Computational Geometry: Theory and Applications
Depth-First Search and Kuratowski Subgraphs
Journal of the ACM (JACM)
Software—Practice & Experience - Special issue on discrete algorithm engineering
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 branch-and-cut approach to the crossing number problem
Discrete Optimization
A New Approach to Exact Crossing Minimization
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Inserting a vertex into a planar graph
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Algorithms and theory of computation handbook
Facets in the Crossing Number Polytope
SIAM Journal on Discrete Mathematics
Journal of Experimental Algorithmics (JEA)
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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 [3]. 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 paper 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 paper is the experimental comparison between the original approach, and these two schemes. We also compare these new results to the solutions of the best known crossing number heuristic.