A graph is 1-planar if it can be drawn in the plane with at most one crossing per edge. The 1-planarity testing problem is NP-complete, even for restricted classes of graphs. We present the first general 1-planarity testing and embedding algorithm, and we experimentally investigate its feasibility in practice. The results suggest that our approach can be successfully applied to graphs with up to 30 vertices, while more sophisticated techniques are needed to attack larger graphs.
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