Inserting an edge into a planar graph

Authors:
Carsten Gutwenger;Petra Mutzel;René Weiskircher
Affiliations:
Max-Planck-Institut für Informatik, Im Stadtwald, 66123 Saarbrücken, Germany;Technische Universität Wien E186, Favoritenstrafβe 9-11, 1040 Wien, Austria;Technische Universität Wien E186, Favoritenstrafβe 9-11, 1040 Wien, Austria
Venue:
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Year:
2001

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Abstract

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 NP-hard. Surprisingly, we found a conceptually simple linear time algorithm based on SPQR trees, which is able to find a crossing minimum solution.