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<p>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.</p>
crossing minimisation; linear embeddings of graphs; circuit layout problems; NP-hard; circuit layout CAD; computational complexity; graph theory; minimisation.

T. Kashiwabara, T. Fujisawa, K. Nakajima and S. Masuda, "Crossing Minimization in Linear Embeddings of Graphs," in IEEE Transactions on Computers, vol. 39, no. , pp. 124-127, 1990.
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