Vertex angle and crossing angle resolution of leveled tree drawings

We study the problem of computing leveled tree drawings, i.e., straight-line drawings of trees where the vertices have distinct preassigned y-coordinates. Our optimization goal is to maximize the crossing angle resolution (i.e., the minimum angle formed by any two crossing edges) and/or the vertex angle resolution (i.e., the minimum angle formed by two edges incident to the same vertex) of the drawing. We provide tight and almost tight worst case bounds for the crossing angle resolution and for the total angle resolution (i.e., the minimum of crossing and vertex angle resolution), respectively.

► We study the angular resolution of leveled tree drawings.
► The minimum crossing angle can always be almost a right angle.
► The total angular resolution decreases with the maximum degree.