Height-preserving transformations of planar graph drawings

Abstract

There are numerous styles of planar graph drawings, such as straight-line drawings, poly-line drawings, orthogonal graph drawings and visibility representations. Given a planar drawing in one of these styles, can it be converted it to another style while keeping the height unchanged? This paper answers this question for (nearly) all pairs of these styles, as well as for related styles that additionally restrict edges to be y-monotone and/or vertices to be horizontal line segments. These transformations can be used to develop new graph drawing results, especially for height-optimal drawings.