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We study the question whether a crossing-free 3D morph between two straight-line drawings of an $n$-vertex tree can be constructed consisting of a small number of linear morphing steps. We look both at the case in which the two given drawings are two-dimensional and at the one in which they are three-dimensional. In the former setting we prove that a crossing-free 3D morph always exists with $O(log n)$ steps, while for the latter $Theta(n)$ steps are always sufficient and sometimes necessary.
Partial edge drawing (PED) is a drawing style for non-planar graphs, in which edges are drawn only partially as pairs of opposing stubs on the respective end-vertices. In a PED, by erasing the central parts of edges, all edge crossings and the result
Human subject studies that map-like visualizations are as good or better than standard node-link representations of graphs, in terms of task performance, memorization and recall of the underlying data, and engagement [SSKB14, SSKB15]. With this in mi
The problem of {em efficiently} finding the best match for a query in a given set with respect to the Euclidean distance or the cosine similarity has been extensively studied in literature. However, a closely related problem of efficiently finding th
Solomon and Elkin constructed a shortcutting scheme for weighted trees which results in a 1-spanner for the tree metric induced by the input tree. The spanner has logarithmic lightness, logarithmic diameter, a linear number of edges and bounded degre
We introduce a model for random geodesic drawings of the complete bipartite graph $K_{n,n}$ on the unit sphere $mathbb{S}^2$ in $mathbb{R}^3$, where we select the vertices in each bipartite class of $K_{n,n}$ with respect to two non-degenerate probab