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Inserting an Edge Into a Planar Graph
 Algorithmica
, 2000
"... 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 ..."
Abstract

Cited by 17 (8 self)
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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 NPhard. Surprisingly, we found a conceptually simple linear time algorithm based on SPQRtrees, which is able to find a crossing minimum solution.