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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.
There are exponentially many $K_5$ and $K_{3,3}$ subgraphs of a $K_n$, never mind minors, so treating them directly isn't terribly efficient. I suggest flipping through said research papers to learn a bit about how other people approach the problem. You should pay attention to properties that (a) give sensible solutions and (b) sound like graphs that interest you.