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Minimum Height Drawings of Ordered Trees in Polynomial Time: Homotopy Height of Tree Duals

2022

We consider drawings of graphs in the plane in which vertices are assigned distinct points in the plane and edges are drawn as simple curves connecting the vertices and such that the edges intersect only at their common endpoints. There is an intuitive quality measure for drawings of a graph that measures the height of a drawing ϕ : G↪ℝ² as follows. For a vertical line 𝓁 in ℝ², let the height of 𝓁 be the cardinality of the set 𝓁 ∩ ϕ(G). The height of a drawing of G is the maximum height over

doi:10.4230/lipics.socg.2022.55
fatcat:ixibqytu7za6peoltj26o5ptvq