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Crossing Minimization in Linear Embeddings of Graphs
January 1990 (vol. 39 no. 1)
pp. 124-127

The problem of embedding a graph in the plane with the minimum number of edge crossings arises in some circuit layout problems. It has been known to be NP-hard in general. Recently, in the area of book embedding, this problem was shown to be NP-hard even when the vertices are placed on a straight line l. The authors show that the problem remains NP-hard even if, in addition to these constraints, the positions of the vertices on l are predetermined.

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Index Terms:
crossing minimisation; linear embeddings of graphs; circuit layout problems; NP-hard; circuit layout CAD; computational complexity; graph theory; minimisation.
S. Masuda, K. Nakajima, T. Kashiwabara, T. Fujisawa, "Crossing Minimization in Linear Embeddings of Graphs," IEEE Transactions on Computers, vol. 39, no. 1, pp. 124-127, Jan. 1990, doi:10.1109/12.46286
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