A Fast Layout Algorithm for k-Level Graphs

In this paper, we present a fast layout algorithm for k-level graphs with given permutations of the vertices on each level. The algorithm can be used in particular as a third phase of the Sugiyama algorithm (1981). The Sugiyama algorithm computes a layout for an arbitrary graph by (1) converting it into a k-level graph, (2) reducing the number of edge crossings by permuting the vertices on the levels, and (3) assigning y-coordinates to the levels and x-coordinates to the vertices. In the layouts generated by our algorithm, every edge will have at most two bends, and will be drawn vertically between these bends