Is there a popular algorithm for the planarization of a non-planar graph.
I'm currently planning to implement a Orthogonal Planar Layout algorithm for undirected graphs in Boost ( Boost Graph Library ). BGL has an implementation to check the planarity of an undirected graph ( Boyer-Myrvold Planarity Testing ) and I plan to use the planar embedding returned by this method to do an orthogonal layout.
But I'm not sure what should be done if the input graph is non-planar. Should I do something with the Kuratowski sub-graph returned in such a scenario to make the graph planar.
A Google Search on "Planarization of non-planar graphs" returns multiple research papers. I'm not sure where to start.