Planar Straight-line Drawings of Layered Digraphs

that every planar graph can be drawn with no edge
crossings and with straight-line edges. We begin this
talk with a review of the literature following Fary's theorem.
Then we consider planar straight-line drawings of layered
digraphs. We show that every ``h-planar'' layered digraph
has a planar straight-line drawing, and that such a drawing
can be obtained in linear time. We conclude by assessing
the possibility that this method could lead to
a competitor to the Sugiyama algorithm.