Boundary Constraints in Force-Directed Graph Layout
Yani Zhang
yanizhang@soe.ucsc.edu
Abstract
When taken constraints as additional input into graph drawing problem, this will lead to
multi-objective optimization problem. The purpose of this report is to summarize the current
state of graph drawing and graph layout algorithms that I have learned in this quarter and to
discuss some interactive applications of graph layout problems which involve boundary
constraints defined by the user. The goal is to allow user to define arbitrary boundaries of a
graph and balance the layout of the current nodes of graph in real time within the defined
boundaries. This algorithm should take boundary as additional input to graph layout problem,
and it should preserve the metal map of the original graph and all users to visualize the
process of graph layout.
Motivation
By examining a range of recently published journal articles, magazine articles and internet
sites on the topic of constrained graphs and its interactive applications, I found several
interactive constraint-based system have been implemented to achieve the goal of
interactively manipulate graph layout, but not many of them try to include outside force or
environment force as boundary constraints. For example, the GLIDE (Graph Layout
Interactive Diagram Editor) system [1] is an editor for drawing medium-sized graphs that
organizes the interaction within a vocabulary of specialized constraints for graph drawing,
but it doesn’t involve manipulation of boundary constraints. There is also a graph
visualization system CGV (Coordinated Graph Visualization) [2], which incorporates several
interactive views that address different aspects of graph visualization. But it didn’t realize
interactively defining boundary of graph either.
Also there are constrains-driven layout algorithms for network diagrams [3] (also known as
node-link diagrams and circle-and-arrow diagrams), which propose a variety of layout
techniques to exhibit the Visual Organization Features (VOFs). VOFs are arrangements of
related nodes in the diagram including horizontal and vertical alignment, axial and radial
symmetries, various shape motifs (e.g., “T”-shaped and hub-shaped motifs), left-to-right and
top-to-bottom sequential placement, and simple node proximity. However, it didn’t constrain
the area where the graph can be laid.
Related Work
Early methods to include boundary constraints are trying to control the size of the graph
layout by assuming that the boundary of the prespecified drawing region acts as a “wall” [4].
And for allow users to interactively contain constraints, they have a constrained graph layout
model which is a generalization of the force-directed model for graph layout [5]. Similar to
force-directed methods, these techniques find a layout minimizing a goal function. Dissimilar
to force-directed methods, constrained graph layout algorithms allow the goal to be
minimized subject to placement constraints on the nodes.
Existing research on graph layout has tended to focus on how to layout a graph statically
using a fixed pre-defined style [6]. Unfortunately, this model of graph layout is not suitable
for interactive applications since when a graph is modified and redisplayed the new layout
may not preserve the mental map of the user and the application program cannot add
constraints on the layout which take into account the underlying semantics of the object
represented by the graph. The layout module takes 3 parameters: the graph G= (V, E), a set
of constraints over the x and y positions of the nodes (the constraints may also refer to other
variables than the node coordinates.), and a partial assignment of suggested values for the
node coordinates. The goal of graph layout module is to find an assignment to variables
representing the node coordinates which is feasible, that is satisfies the constraints, gives a
good layout, and assigns values to the variables which are as close as possible to the
suggested values [7].
Proposed Research Direction
The original graph I will consider force-directed approach which uses a physical model
where the vertices and edges of the graph are viewed as objects subject to various forces. The
boundaries defined by the user will represented by lines which are linked between two nodes,
and lines linked together as boundaries. The users can manipulate those nodes to change the
shape of the boundaries. I will first try unit repelling forces on the boundary, and push the
original graph inside it. And for each node of the original graph, after adding all the forces to
it, I will recalculate their positions inside the boundary and show the process of changing to a
new layout.
Reference
[1] Ryall, Kathy, Joe Marks, and Stuart Shieber. "An interactive constraint-based system for
drawing graphs." Proceedings of the 10th annual ACM symposium on User interface
software and technology. ACM, 1997.
[2] Tominski, Christian, James Abello, and Heidrun Schumann. "CGV—An interactive
graph visualization system." Computers & Graphics 33.6 (2009): 660-678.
[3] P. Eades and R. Tamassia. Algorithms for drawing graphs: An annotated bibliography.
Technical Report CS-89-09, Department of Computer Science, Brown University, October
1989. Revised version.
[4] Fruchterman, Thomas MJ, and Edward M. Reingold. "Graph drawing by force‐directed
placement." Software: Practice and experience 21.11 (1991): 1129-1164.
[5] He, Weiqing, and Kim Marriott. "Constrained graph layout." Graph Drawing. Springer
Berlin/Heidelberg, 1997.
[6] Kamps, Thomas, Joerg Kleinz, and John Read. "Constraint-based spring-model algorithm
for graph layout." Graph drawing. Springer Berlin/Heidelberg, 1996.
[7] Dwyer, Tim, Kim Marriott, and Michael Wybrow. "Topology preserving constrained
graph layout." Graph Drawing. Springer Berlin/Heidelberg, 2009.