414 CHAPTER 13. HIERARCHICAL DRAWING ALGORITHMS
13.2.1 Heuristics Based on Vertex Orderings
As we mentioned above any linear ordering of the vertices provides two FSs. Imagine the
vertices placed on a horizontal line in accordance with the provided linear ordering. The
first FS consists of the edges with direction from left to right, and the second FS consists
of the edges with direction from right to left. It can be shown that there are digraphs and
linear orderings of the vertices for which both FSs have the same size [BS90]. Thus, the
simple approach is a 2-approximation heuristic for solving both the minimum FS and FAS
problems.
It is clear that the outcome of this simple approach depends on the linear ordering of the
vertices. Some researchers hav ...