On embedding a graph in the grid with the minimum number of bends
SIAM Journal on Computing
On the complexity of covering vertices by faces in a planar graph
SIAM Journal on Computing
SIAM Journal on Computing
An experimental comparison of four graph drawing algorithms
Computational Geometry: Theory and Applications
Computing Orthogonal Drawings with the Minimum Number of Bends
IEEE Transactions on Computers
Optimizing over All Combinatorial Embeddings of a Planar Graph
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Computing Optimal Embeddings for Planar Graphs
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
Drawing High Degree Graphs with Low Bend Numbers
GD '95 Proceedings of the Symposium on Graph Drawing
A Linear Time Implementation of SPQR-Trees
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
On the Compuational Complexity of Upward and Rectilinear Planarity Testing
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Some Applications of Orderly Spanning Trees in Graph Drawing
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
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We consider the problem of minimizing the number of bends in an orthogonal planar graph drawing. While the problem can be solved via network flow for a given planar embedding of a graph G, it is NP-hard if we consider the set of all planar embeddings of G. Our approach combines an integer linear programming (ILP) formulation for the set of all embeddings of a planar graph with the network flow formulation for fixed embeddings. We report on computational experiments on a benchmark set containing hard problem instances that was already used for testing the performance of a previously published branch & bound algorithm for solving the same problem. Our new algorithm is about twice as fast as the branch & bound approach for the graphs of the benchmark set.