Drawing Graphs with Vertices at Specified Positions and Crossings at Large Angles
In point-set-embeddability (PSE) problems one is given not just a graph that is to be drawn, but also a set of points in the plane that specify where the vertices of the graph can be placed. The problem class was introduced by Gritzmann et al.  twenty years ago. In their work and most other works on PSE problems, however, planarity of the output drawing was an essential requirement. Recent experiments on the readability of drawings  showed that polyline drawings with angles at edge crossings close to 90°. and a small number of bends per edge are just as readable as planar drawings. Motivated by these findings, Didimo et al.  recently introduced RAC drawings where pairs of crossing edges must form a right angle and, more generally, αAC drawings (for α ∈ (0, 90°]) where the crossing angle must be at least α. As usual, edges may not overlap and may not go through vertices. We investigate the intersection of PSE and RAC/αAC.
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