| C. Gutwenger, P. Mutzel, and R. Weiskircher. Inserting an edge into a planar graph. In Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '2001), pages 246--255, Washington, DC, 2001. ACM Press. |
....On the other hand, it is time consuming to implement the approach, since many di erent kinds of algorithms are needed. Recently, a lot of research has been done to solve many of the upcoming problems. Major improvements have been made concerning various aspects of the planarisation phase, e.g. [3 5], the orthogonalisation phase, e.g. 6 9] and the compaction phase [10, 11] Moreover, today there exist some software libraries containing the topology shape metrics approach [12 15] Often it is implemented in a modular form, so that it is easy to experiment with. This enables experimental ....
C. Gutwenger, P. Mutzel, and R. Weiskircher. Inserting an edge into a planar graph. Technical report, Technische Universitat Wien, 2000. Submitted for publication.
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C. Gutwenger, P. Mutzel, and R. Weiskircher. Inserting an edge into a planar graph. In Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '2001), pages 246--255, Washington, DC, 2001. ACM Press.
....all necessary algorithms and data structures, since the planarization method consists of various phases in which complex algorithms appear. Recently, major improvements have been made concerning the use of the planarization method in practice (e.g. JM96b, FK96, GM98, KM99, BDD 00, GM00, GMW00] Today, there exist some (publically available) software libraries using the planarization method successfully for practical graph layout [AGD00, GDT, GT98] In AGD, the planarization method is implemented in a modular form, so that it is easy to experiment with di erent approaches to the ....
....insert the edges iteratively while keeping the embedding xed. This method is implemented in AGD as module ShortestPathInserter. However, xing the embedding can lead to many more crossings than necessary even if only one edge needs to be reinserted. Recently, Gutwenger, Mutzel, and Weiskircher [GMW00] have presented a conceptually simple linear time algorithm (based on SPQR trees) for inserting an edge into a planar graph with the minimum number of crossings over the set of all combinatorial embeddings. In AGD, this algorithm is implemented in the module OneEdgeMinCrossInserter. Rather than ....
C. Gutwenger, P. Mutzel, and R. Weiskircher. Inserting an edge into a planar graph. Technical report, Technische Universitat Wien, 2000. Submitted for publication.
....other hand, great e ort is needed to implement all necessary algorithms and data structures, since the planarization method consists of various phases in which complex algorithms appear. Recently, major improvements have been made concerning the use of the planarization method in practice (e.g. [32, 17, 24, 38, 4, 25, 26]) Today, there exist some (publically available) software libraries using the planarization method successfully for practical graph layout [1, 20, 21] In AGD, the planarization method is implemented in a modular form, so that it is easy to experiment with di erent approaches to the various ....
....43 44 45 46 47 48 (b) Optimal embedding Figure 3: The in uence of the combinatorial embedding module ShortestPathInserter. However, xing the embedding can lead to many more crossings than necessary even if only one edge needs to be reinserted. Recently, Gutwenger, Mutzel, and Weiskircher [26] have presented a conceptually simple lineartime algorithm (based on SPQR trees) for inserting an edge into a planar graph P with the minimum number of crossings over the set of all combinatorial embeddings. In AGD, this algorithm is implemented in the module OneEdgeMinCrossInserter. Rather than ....
C. Gutwenger, P. Mutzel, and R. Weiskircher. Inserting an edge into a planar graph. Technical report, Technische Universitat Wien, 2000. Submitted for publication.
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