Advances in the Planarization Method: Effective Multiple Edge Insertions

Abstract

The planarization method is the strongest known method to heuristically find good solutions to the general crossing number problem in graphs: Starting from a planar subgraph, one iteratively inserts edges, representing crossings via dummy vertices. In the recent years, several improvements both from the practical and the theoretical point of view have been made. We review these advances and conduct an extensive study of the algorithms' practical implications. Thereby, we also present the first implementation of an approximation algorithm for the crossing number problem of general graphs. We compare the obtained results with known exact crossing number solutions and show that modern techniques allow surprisingly tight results in practice.