Vertex angle and crossing angle resolution of leveled tree drawings

Authors:
Walter Didimo;Michael Kaufmann;Giuseppe Liotta;Yoshio Okamoto;Andreas Spillner
Affiliations:
Universití di Perugia, Italy;Universität Tübingen, Germany;Universití di Perugia, Italy;University of Electro-Communications, Japan;Universität Greifswald, Germany
Venue:
Information Processing Letters
Year:
2012

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Abstract

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.