The most common commercial technique for drawing directed graphs invol
ves partitioning the vertex set V into ''layers'' L(1), L(2),...,L(k).
Vertices in L(i) are arranged on the horizontal line y = i. A signifi
cant problem for such drawings is to choose an arrangement within each
layer so that crossings are avoided. In this talk we discuss the comp
utational complexity of choosing such an arrangement.