Abstract
Giordano, Liotta and Whitesides [1] developed an algorithm that, given an embedded planar st-digraph and a topological numbering ρ of its vertices, computes in O(n2) time a ρ-constrained upward topological book embedding with at most 2n–4 spine crossings per edge. The number of spine crossings per edge is asymptotically worst case optimal.
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References
Giordano, F., Liotta, G., Whitesides, S.H.: Embeddability Problems for Upward Planar Digraphs. In: Tollis, I.G., Patrignani, M. (eds.) GD 2008. LNCS, vol. 5417, pp. 242–253. Springer, Heidelberg (2009)
Mchedlidze, T., Symvonis, A.: Crossing-optimal acyclic hamiltonian path completion and its application to upward topological book embeddings. In: Das, S., Uehara, R. (eds.) WALCOM 2009. LNCS, vol. 5431, pp. 250–261. Springer, Heidelberg (2009)
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Mchedlidze, T., Symvonis, A. (2010). On ρ-Constrained Upward Topological Book Embeddings. In: Eppstein, D., Gansner, E.R. (eds) Graph Drawing. GD 2009. Lecture Notes in Computer Science, vol 5849. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11805-0_40
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