Crossing Reduction for Hierarchical Graphs with Intra-Level Edges

In drawings of hierarchical graphs generated by the conventional Sugiyama framework the vertices are positioned on multiple horizontal level lines. This drawing style which allows edges only between vertices on different levels is well suited for the visualization of a common direction of flow from lower to higher levels in a graph. In this paper we are interested in reordering the vertices on each level line to increase readability of the drawing, i. e., in reducing the number of edge crossings. As novelty, we additionally allow the existence of edges with both end vertices on a common level, which often occur in practice. Experimentally we found out, that we can save about 30% of the crossings compared to the existing standard heuristic which ignores those edges.