5 Graph Description Language (GDL) - Absint

The ordering of nodes within one level influences the weights of the adjacent levels, consequently
this is performed iteratively until a user-defined maximum is reached or no more improvements
are recognized. This is phase 1 of the crossing reduction.
If the weights of some nodes are equal a permutation of these nodes is tried. Sometimes a permutation
enables crossings to be reduced even further (optional phase 2 of crossing reduction).
There are four possibilities to calculate weights for crossing heuristics. The default weights are
barycenter weights [STM81], while mediancenter weights [GNV88] are sometimes more appropriate,
especially if the average degree (number of edges) of nodes is small. barymedian weights
are the combination of barycenter and mediancenter, where barycenter is considered first and mediancenter
is only used for nodes whose barycenter weights are equal. Conversely, medianbary
weights are the combination of barycenter and mediancenter, where mediancenter is considered
first. The weights can be selected interactively in the Layout dialog box, or statically in the GDL
specification. See graph attribute crossing_weight (p. 69).
However, the final result needn’t necessarily be optimal as crossing reduction is only a heuristic.
Finally, a local optimization phase tries to improve the layout by exchanging directly neighbored
nodes. See graph attribute crossing_optimization (p. 69)
6.4.3 Coordinate Calculation
Coordinate calculation follows after partitioning nodes into levels and ordering the nodes within
the levels. Nodes can be aligned at the bottom or at the top of a level or centered at a level, with
there being a minimum distance between levels (yspace). This influences the y coordinates. The x
coordinate has to be calculated such that there is a minimum distance between nodes (xspace) and
a minimum distance between the bend points of edges (xlspace). Furthermode, the layout should
be balanced such that the edges are short and straight.
This achieved by using a special method for downward laid-out trees or performing two general
iteration phases: The first phase simulates a physical pendulum, the nodes being the balls and the
edges the strings. The balls hanging on the strings swing to and fro, i.e. the nodes move within
their level and influence the neighboring nodes until the layout is sparse enough and each node has
sufficient space to be favorably positioned.
Next the nodes are centered with respect to their edges. This phase simulates a rubberband network:
The edges pull on a node with a power proportional to their length, the result being that the
node moves to a position such that the sum of the forces of its edges is zero. Then, the length of
the edges is balanced.
An optional fine-tuning phase tries to recognize long edges and draws them as vertical long line
segments. This is useful for the orthogonal layout methods.
Unfortunately, both physical simulations needn’t be convergent, meaning they may be iterated
infinitely often without resulting in a stable layout. However, these cases are seldom. The number
of iterations is restricted in order to prevent infinite execution, the t message indicating that a
timeout has occurred.
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