The one-sided two-level crossing reduction problem is an important problem in hierarchical graph drawing. Because of its NP-hardness there are many heuristics, such as the well-known barycenter and median heuristics. We consider the constrained one-sided two-level crossing reduction problem, where the relative position of certain vertex pairs on the second level is fixed. Based on the barycenter heuristic, we present a new algorithm that runs in quadratic time and generates fewer crossings than existing simple extensions. It is significantly faster than an advanced algorithm by Schreiber and Finnocchi, while it compares well in terms of crossing number. It is also easy to implement.
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