An effective crossing minimisation heuristic based on star insertion

We present a new heuristic method for minimising crossings in a graph. The method is based upon repeatedly solving the so-called {\em star insertion problem} in the setting where the combinatorial embedding is fixed, and has several desirable characteristics for practical use. We introduce the method, discuss some aspects of algorithm design for our implementation, and provide some experimental results. The results indicate that our method compares well to existing methods, and also that it is suitable for dense instances.