5 Graph Description Language (GDL) - Absint

• Gravitational forces
The problem with spring forces is that they are only effective in connected graphs. In unconnected
graphs simulating a spring embedder makes unconnected nodes move away from one
another as there are only repulsive forces but no attractive forces. That is why gravitational
forces are introduced. All nodes are attracted to the bary center of all the other nodes.
• Simulated annealing
The simulated annealing model is oriented to the physical process of annealing, which often
leads to very regular structures (e.g. like crystals).
A global energy level is computed for a graph which is the sum of all energy levels of the
nodes. The energy level at a node is determined from the forces acting it, much like the
elongation of the springs. The spring embedder tries to minimize the global energy level by
moving the nodes in the direction of the forces.
Nodes are randomly moved so as to avoid being trapped at a local energy minimum. At the
beginning this is done more vigorously, with random movement being ceased towards the
end in order to stabilize the final layout. The amount of random movement depends on the
”temperature”, which is controlled by a temperature scheme.
aiSee also supports the concept of local temperatures for a node. The temperature takes the
local situation of the graph into account (see energetic graph attribute, p. 70) and regulates
how much and how often a node is randomly moved.
The force-directed placement algorithm consists of four phases:
• Initialization phase
• First iteration phase
• Optional second iteration phase
• Final improvement phase
The two iteration phases are conceptionally the same. They simply sequentially simulate the two
magnetic fields acting on the system. The second iteration phase is omitted if there is only one
magnetic field.
One iteration phase consists of a loop of iteration steps that are executed until the global temperature
value has fallen below a specified threshold value or until a maximum number of iterations is
reached.
In each iteration step the new impulses of the nodes (force directions) are calculated, the nodes
moved to their new positions according to the impulses, and the global temperature adjusted.
In the final improvement phase, the node positions can be rastered. This is done by moving a node
to its closest raster point after each iteration step.
Finally the minimum x and y coordinates are calculated and the entire layout is moved so that
the minimum coordinates are just zero. This step is necessary because all nodes move during the
iteration phase, meaning they could have all moved away from the origin of the coordinate system.
Finally the start and end points of the edges are calculated.
For more details, see [Sa96].
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