Inserting an Edge into a Planar Graph

Carsten Gutwenger, Petra Mutzel, René Weiskircher
2005 Algorithmica  
Computing a crossing minimum drawing of a given planar graph G augmented by an additional edge e in which all crossings involve e, has been a long standing open problem in graph drawing. Alternatively, the problem can be stated as finding a planar combinatorial embedding of a planar graph G in which the given edge e can be inserted with the minimum number of crossings. Many problems concerned with the optimization over the set of all combinatorial embeddings of a planar graph turned out to be
more » ... -hard. Surprisingly, we found a conceptually simple linear time algorithm based on SPQR-trees, which is able to find a crossing minimum solution.
doi:10.1007/s00453-004-1128-8 fatcat:pteako5g6zhe3o7k3cfqopvw2a