Bend Minimization in Orthogonal Drawings Using Integer Programming

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.