5 Graph Description Language (GDL) - Absint

sorting to assign ranks to nodes. This is much faster, however it requires that the graph be
acyclic.
• tree:
This method is very fast, however it can’t be used unless the graph is a forest of downward
laid-out trees. A downward laid-out tree has the following structure: Each node at rank l
has at most one adjacent edge coming from a node of an upper rank k < l. A node may have
edges pointing to nodes at the same level and edges coming from nodes of lower ranks k > l.
The direction of the edges may be arbitrary, but the picture of the layout (if the arrow heads
are ignored) has to be a tree (see Figure 31). The assignment of ranks is done by DFS. Then,
the graph is checked to determine whether it is a forest of downward laid-out trees. If this
is not the case, the standard layout is used as a fallback solution. Crossing reduction (see
next section) is not necessary for downward laid-out trees, meaning a very fast positioning
algorithm can be used.
Figure 31: Downward Laid-out Trees and Structural Trees
A further possibility for influencing the layout is edge priority. Higher priority edges are preferable
when calculating the spanning tree. After partitioning, a fine-tuning phase tries to improve the
ranks in order to avoid very long edges.
6.4.2 Crossing Reduction
This pass calculates a good order of the nodes within levels ao as to avoid edge crossings. The first
step is to separate connected components of the graph and to handle each component separately.
The crossing reduction algorithm calculates the weights of the nodes in keeping with the possible
crossings to the left and the right, and reorders the nodes of a level according to these weights.
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