Journal of Graph Algorithms and Applications
http://jgaa.info/ vol. 14, no. 1, pp. 53–74 (2010)
Efficient, Proximity-Preserving Node Overlap
Removal
Emden R. Gansner Yifan Hu
AT&T Labs,
Shannon Laboratory,
180 Park Ave.,
Florham Park, NJ 07932.
Abstract
When drawing graphs whose nodes contain text or graphics, the nontrivial node sizes must be taken into account, either as part of the initial
layout or as a post-processing step. The core problem in avoiding or
removing overlaps is to retain the structural information inherent in a
layout while minimizing the additional area required. This paper presents
a new node overlap removal algorithm that does well at retaining a graph’s
shape while using little additional area and time. As part of the analysis,
we consider and evaluate two measures of dissimilarity for two layouts of
the same graph.
Submitted:
November 2008
Reviewed:
March 2009
Final:
November 2009
Article type:
Regular paper
Revised:
Accepted:
May 2009
November 2009
Published:
January 2010
Communicated by:
I. G. Tollis and M. Patrignani
E-mail addresses: erg@research.att.com (Emden R. Gansner) yifanhu@research.att.com (Yifan
Hu)
54
Gansner and Hu Efficient Node Overlap Removal
1
Introduction
Most existing symmetric graph layout algorithms treat nodes as points. In
practice, nodes usually contain labels or graphics that need to be displayed.
Naively incorporating this can lead to nodes that overlap, causing information
of one node to occlude that of others. If we assume that the original layout
conveys significant aggregate information such as clusters, the goal of any layout
that avoids overlaps should be to retain the “shape” of the layout based on point
nodes.
The simplest and, in some sense, the best solution is to scale up the drawing
while preserving the node size until the nodes no longer overlap [30]. This has
the advantage of preserving the shape of the layout exactly, but can lead to
inconveniently large drawings. In general, overlap removal is typically a tradeoff between preserving the shape and limiting the area, with scaling at one
extreme.
Many techniques to avoid overlapping nodes have been devised. One approach is to make the node size part of the model of the layout algorithm. It
is assumed that whatever structure that would have been exposed using point
nodes will still be evident in these more general layouts. For hierarchical layouts, the node size can be naturally incorporated into the algorithm [11, 35].
For symmetric layouts, various authors [3, 19, 28, 37] have extended the springelectrical model [7, 12] to take into account node sizes, usually as increased repulsive forces. Node overlap removal can also be built into the stress model [26]
by specifying the ideal edge length to avoid overlap along the graph edges. Such
heuristics, however, cannot guarantee all overlaps will be removed, so they typically rely on overly large repulsive forces, or the type of post-processing step
considered below. This problem was addressed by Dwyer et al. [5], who showed
how to encode overlap avoidance, as well as many other layout features, as linear constraints in a stress function, and then optimize the stress function using
stress majorization [13].
An alternative approach is to remove node overlaps as a post-processing
step after the graph is laid out. Here the trade-off between layout size and
preserving the graph’s shape is more explicit. In addition to many of the algorithms mentioned above that can be adapted for this use, a number of other
algorithms have been proposed. For example, the Voronoi cluster busting algorithm [15, 29] works by iteratively forming a Voronoi diagram from the current
layout and moving each node to the center of its Voronoi cell until no overlaps
remain. The idea is that restricting each node to its corresponding Voronoi
cell should preserve the relative positions of the nodes. In practice, because of
the number of iterations often required and the use of a rectangular bounding
box,1 the nodes in the final drawing can be homogeneously distributed within
a rectangle, the graph bearing little resemblance to the original layout.
Another group of post-processing algorithms is based on setting up pairwise
node constraints to remove overlaps and then performing some procedure to
1 The latter might be improved by using something like α-shapes [8] to provide a more
accurate boundary.
JGAA, 14(1) 53–74 (2010)
55
generate a feasible solution. The force scan algorithm [31] and its later variants [20, 24] proceed along these lines. More recently, Marriott et al. [30, 31]
have presented quadratic programming algorithms which remove node overlaps
while, if desired, minimizing node displacement. All of these techniques rely
on solving separate horizontal and vertical problems. They behave differently
if the layout is rotated by a degree that is not a multiple of π/2. We have also
found that, in practice, this asymmetry often results in a layout with a distorted
aspect ratio (e.g., Figure 4, bottom right).
One desideratum proposed [31] for overlap removal is the preservation of
orthogonal ordering, i.e., the relative ordering of the x and y coordinates of
two nodes should be the same in the original layout and the one with overlaps
removed. Thus, if a node is above and to the left of another node in the original
layout, it is above and to the left in the derived one. The idea is that, in
this manner, a user’s “mental map” of the graph is better preserved. Many of
the algorithms described above either inherently preserve orthogonal ordering,
or have simple variations that do. While preserving orthogonal ordering can
be important, it alone cannot ensure that the relative proximity relations [23]
between nodes are preserved. At other times, it is too restrictive, causing two
highly-related nodes to be moved far apart due to some largely unrelated third
node. For these reasons, our approach is to concentrate on proximity relations
and not deal with orthogonal ordering.
In this paper, we focus on the problem of removing overlaps rather than
avoiding them. To this end, we discuss (Section 3) metrics for the similarity
between two layouts which we believe better quantify the desired outcome of
overlap removal than minimized displacement or such simpler measures as aspect ratio or edge ratio (the ratio of the longest and the shortest edge lengths).
We then present (Section 4) a node overlap removal algorithm based on a proximity graph of the nodes in the original layout. Using this graph as a guide,
it iteratively moves the nodes, particularly those that overlap, while keeping
the relative positions between them as close to those in the original layout as
possible. The algorithm is similar to the stress model [26] used for graph layout,
except that the stress function involves only a sparse selection of all possible
node pairs. Because of this sparse stress function, the algorithm is efficient and
is able to handle very large graphs. In Section 5, we evaluate our algorithm
and others using the proposed similarity measures. Finally, Section 6 presents
a summary and topics for further study.
2
Background
We use G = (V, E) to denote an undirected graph, with V the set of nodes
(vertices) and E edges. We use |V | and |E| for the number of vertices and
edges, respectively. We let xi represent the current coordinates of vertex i
in Euclidean space. For this paper we are interested in 2D layout, therefore
xi ∈ R2 .
The aim of graph drawing is to find xi for all i ∈ V so that the resulting
56
Gansner and Hu Efficient Node Overlap Removal
drawing gives a good visual representation of the information in the graph. Two
popular methods, the spring-electrical model [7, 12], and the stress model [26],
both convert the problem of finding an optimal layout to that of finding a
minimal energy configuration of a physical system. We shall describe the stress
model in more detail since we will use a similar model for the purpose of node
overlap removal in Section 4.
The stress model assumes that there are springs connecting all nodes of
the graph, with the ideal spring length equal to the graph theoretical distance
between nodes. The energy of this spring system is
X
wij (kxi − xj k − dij ) 2 ,
(1)
i6=j
where dij is the graph theoretical distance between vertices i and j, and wij is a
weight factor, typically 1/dij 2 . The layout that minimizes the above stress energy is an optimal layout of the graph. There are several ways to find a solution
of the minimization problem. An iterative approach can be employed. Starting
from a random layout, the total spring force on each vertex is calculated, and
the vertex is moved along the direction of the force for a certain step length.
This process is repeated, with the step length decreasing every iteration, until
the layout stabilizes. Alternatively, a stress majorization technique can be employed, where the cost function (1) is bounded by a series of quadratic functions
from above, and the process of finding an optimum becomes that of solving a
series of linear systems [13].
In the stress model, the graph theoretical distance between all pairs of vertices has to be calculated, leading to quadratic complexity in the number of
vertices. There have been attempts (e.g., [2, 13]) to simplify the stress function
by considering only a sparse portion of the graph. Our experience, however,
with real-life graphs is that these techniques may fail to yield good layouts.
Therefore, algorithms based on a spring-electrical model employing a multilevel approach and an efficient approximation scheme for long range repulsive
forces [18, 22, 36] are still the most efficient choices to lay out large graphs
without consideration of the node size.
3
Measuring Layout Similarity
The outcome of an overlap removal algorithm should be measured in two aspects.
The first aspect is the overall bounding box area: we want to minimize the area
taken by the drawing after overlap removal. The second aspect is the change
in relative positions. Here we want the new drawing to be as “close” to the
original as possible. It is this aspect that is hard to quantify.
When total node movement is optimized [6, 24], comparison is reduced to
measuring the amount of displacement of the vertices in the new layout from
those of the original graph. This measurement does not take into account possible shifts, scalings or rotations, nor the importance of maintaining the relative
position among vertices.
JGAA, 14(1) 53–74 (2010)
57
As far as we are aware, there is no definitive way to measure similarity of
two layouts of the same graph. We adopt two approaches. The first approach
is based on measuring changes in lengths of edges. The second approach, which
is a modification of the metric of Dwyer et al. [6], is based on measuring the
displacement of vertices, after discounting shift, scaling and rotation.
Before defining these two measures of similarity, we first introduce the concept of a proximity graph. A proximity graph is a graph derived from a set of
points in space: points that are “neighbors” to each other in the space form
an edge in the proximity graph. There are many ways to create a proximity
graph [25]. In this paper, we shall work with the Delaunay triangulation (DT),
which is an approximation to the proximity graph, and has the advantage being
rigid. Two points are neighbors in DT if and only if there exists a sphere passing
through these two points, and no other points lie in the interior of this sphere.
One way to measure the similarity of two layouts is to measure the distance
between all pairs of vertices in the original and the new layout. If the two
layouts are similar, then these distances should match, subject to scaling. This
is known as Frobenius metric in the sensor localization problem [9]. Calculating
all pairwise distances is expensive for large graphs, both in CPU time and in
the amount of memory. As we want a metric feasible for very large graphs, we
instead form a DT of the original graph, then measure the distance between
vertices along the edges of the triangulation for the original and new layouts.2
If x0 and x denote the original and the new layout, and EP is the set of edges
in the triangulation, we calculate the ratio of the edge length
rij =
kxi − xj k
, {i, j} ∈ EP ,
kx0i − x0j k
then define a measure of the dissimilarity as the normalized standard deviation
rP
(rij −r̄)2
|EP |
{i,j}∈EP
σdist (x0 , x) =
r̄
,
where
r̄ =
1
|EP |
X
rij
{i,j}∈EP
is the mean ratio.
The reason we measure the edge length ratio along edges of the proximity
graph, rather than along edges of the original graph, is that if the original
graph is not rigid, then even if two layouts of the same graph have the same
edge lengths, they could be completely different. For example, think of the
graph of a square, and a new layout of the same graph in the shape of a nonsquare rhombus. These two layouts may have exactly the same edge lengths,
2 Another possibility would be to sample O(|V |) out of the |V |(|V | − 1)/2 possible vertex
pairs. Some care is needed in making sure that the resulting graph is rigid.
58
Gansner and Hu Efficient Node Overlap Removal
4
3
4
1
2
1
3
2
Figure 1: The edge lengths of these two layouts of a non-rigid graph are exactly
the same, but the layouts are clearly different.
but are clearly different (see Figure 1). The rigidity of the triangulation avoids
this problem.
Notice that σdist (x0 , x) is not symmetric with regard to which layout comes
first. Furthermore, in theory, this non-symmetric version could class a layout
and a foldover of it (e.g., a square grid with one half folded over the other) as
the same. We can symmetrize it by defining the dissimilarity between layout x
and x0 as (σdist (x0 , x) + σdist (x, x0 ))/2. This also resolves the “foldover problem”. The symmetric version may be more appropriate if we are comparing two
unrelated layouts. Since, however, we are comparing a layout derived from an
existing layout, we feel that the asymmetric version is adequate.
An alternative measure of similarity is to calculate the displacement of vertices of the new layout from the original layout [6]. Clearly a new layout derived
from a shift, scaling and rotation should be considered identical. Therefore we
modify the straight displacement calculation by discounting the aforementioned
transformations. This is achieved by finding the optimal scaling, shift and rotation that minimize the displacement. The optimal displacement is then a
measure of dissimilarity.
We denote by scalars r and θ the scaling and rotation,
cos(θ) sin(θ)
T =
(2)
− sin(θ) cos(θ)
the rotation matrix, p ∈ R2 the translation, and define the displacement dissimilarity as
X
σdisp (x0 , x) = minp∈R2 ,θ,r∈R
krT xi + p − x0i k2 ,
(3)
i∈V
This is a known problem in the Procrustes analysis [1, 16] and the solution (the
Procrustes statistic) is
T
T
1
σdisp (x0 , x) = tr(X 0 X 0 ) − (tr((X T X 0 X 0 X) 2 )2 tr(X T X),
(4)
where tr(A) is the trace of a matrix A, X is a matrix with columns xi − x̄, X 0
is a matrix with columns x0i − x̄0 , and x̄ and x̄0 are the centers of gravity of the
new and original layout.
JGAA, 14(1) 53–74 (2010)
59
j
j
i
i
Figure 2: Nodes i and j overlap (left). The overlap factor, according to (5), is
min((2 + 2)/3, (1 + 2)/2) = 1.33. Expanding the edge i − j by 33% removes the
overlap (right).
In the above we do not consider shearing, since we believe a layout derived
from shearing of the original should not be considered identical to the latter.
The quality of an overlap removal algorithm is a combination of how similar
the new layout is to the original, and how small an area it occupies. The
simplest overlap removal algorithm is that of scaling the layout until all overlaps
are removed. This has a dissimilarity of 0, but usually occupies a very large
area. The alternative extreme is to pack the nodes as close to each other as
possible while ignoring the original layout. This will have the smallest area, but
a large dissimilarity. A good solution should be a compromise between these
two extremes. We now describe one candidate.
4
A Proximity Stress Model for Node Overlap
Removal
Our goal is to remove overlaps while preserving the shape of the initial layout by
maintaining the proximity relations [23] among the nodes. To do this, we first
set up a rigid “scaffolding” structure so that while vertices can move around,
their relative positions are maintained. This scaffolding is constructed using an
approximate proximity graph, in the form of a Delaunay triangulation (DT).
Once we form a DT, we check every edge in it and see if there are any node
overlaps along that edge. Let wi and hi denote the half width and height of
the node i, and x0i (1) and x0i (2) the current X and Y coordinates of this node.
If i and j form an edge in the DT, we calculate the overlap factor of these two
nodes
tij = max min
hi + hj
wi + wj
,
|x0i (1) − x0j (1)| |x0i (2) − x0j (2)|
!
!
,1 .
(5)
For nodes that do not overlap, tij = 1. For nodes that do overlap, such overlaps
can be removed if we expand the edge by this factor, see Figure 2. Therefore
we want to generate a layout such that an edge in the proximity graph has the
60
Gansner and Hu Efficient Node Overlap Removal
ideal edge length close to tij kx0i − x0j k. In other words, we want to minimize the
following stress function
X
wij (kxi − xj k − dij ) 2 .
(6)
(i,j)∈EP
Here dij = sij kx0i − x0j k is the ideal distance for the edge {i, j}, sij is a scaling
factor related to the overlap factor tij (see (7)), wij = 1/kdijk2 is a weighting
factor, and EP is the set of edges of the proximity graph. We call (6) the
proximity stress model in obvious analogy.
Because DT is a planar graph, which has no more than 3|V | − 6 edges, the
above stress function has no more than 3|V | − 6 terms. Furthermore, because
DT is rigid, it provides a good scaffolding that constrains the relative position
of the vertices and helps to preserve the global structure of the original layout.
It is important that we do not attempt to remove overlaps in one iteration
by using the above model with sij = tij . Imagine the situation of a regular mesh
graph, with one node i of particularly large size that overlaps badly with its
nearby nodes, but the other nodes do not overlap with each other. Suppose
nodes i and j form an edge in the proximity graph, and they overlap. If we
try to make the length of the edge equal tij kx0i − x0j k, we will find that tij is a
number much larger than 1, and the optimum solution to the stress model is to
keep all the other vertices at or close to their current positions, but move the
large node i outside of the mesh, at a position that does not cause overlap. This
is not desirable because it destroys the original layout. Therefore we damp the
overlap factor by setting
sij = min(tij , smax )
(7)
and try to remove overlap a little at a time. Here smax > 1 is a number limiting
the amount of overlap we are allowed to remove in one iteration. We found that
smax = 1.5 works well.
After minimizing (6), we arrive at a layout that may still have node overlaps.
We then regenerate the proximity graph using DT and calculate the overlap
factor along the edges of this graph, and redo the minimization. This forms an
iterative process that ends when there are no more overlaps along the edges of
the proximity graph.
For many graphs, the above algorithm yields a drawing that is free of node
overlaps. For some graphs, however, especially those with nodes having extreme
aspect ratios, node overlaps may still occur. Such overlaps happen for pairs of
nodes that are not near each other, and thus do not constitute edges of the
proximity graph. Figure 3(a) shows the drawing of a graph after minimizing
(6) iteratively, so that no more node overlap is found along the edges of the
Delaunay triangulation. Clearly, node 2 and node 4 still overlap. If we plot
the Delaunay triangulation (Figure 3(b)), it is seen that nodes 2 and 4 are not
neighbors in the proximity graph, which explains the overlap.
To overcome this situation, once the above iterative process has converged
so that no more overlaps are detected over the DT edges, we apply a scan-
JGAA, 14(1) 53–74 (2010)
8
7
6
9
8
5
1
2 with a
tall
label
6
9
5
11
10
7
61
11
4 with an extremely looong label
3
10
1
2 with a
tall
label
4 with an extremely looong label
3
Figure 3: (a): A graph layout where nodes 2 and 4 overlap. (b): the proximity
graph (Delaunay triangulation) of the current layout. No two nodes linked by
an edge of the proximity graph overlap.
line algorithm [6] to find all overlaps, and augment the proximity graph with
additional edges, where each edge consists of a pair of nodes that overlap. We
then re-solve (6). This process is repeated until the scan-line algorithm finds
no more overlaps. We call our algorithm PRISM (PRoxImity Stress Model).
Algorithm 1 gives a detailed description of this algorithm.
Algorithm 1 Proximity stress model based overlap removal algorithm (PRISM)
Input: coordinates for each vertex, x0i , and bounding box width and height
{wi , hi }, i = 1, 2, . . . , |V |.
repeat
Form a proximity graph GP of x0 by Delaunay triangulation.
Find the overlap factors (5) along all edges in GP .
Solve the proximity stress model (6) for x. Set x0 = x.
until (no more overlaps along edges of GP )
repeat
Form a proximity graph GP of x0 by Delaunay triangulation.
Find all node overlaps using a scan-line algorithm. Augment GP with edges
from node pairs that overlap.
Find the overlap factor (5) along all edges of GP .
Solve the proximity stress model (6) for x. Set x0 = x.
until (no more overlaps)
We now discuss some of the main computational steps in the above algorithm. Delaunay triangulation can be computed in O(|V | log |V |) time [10, 17,
27]. We used the mesh generator Triangle [33, 34] for this purpose.
The scan-line algorithm can be implemented to find all the overlaps in
O(l|V |(log |V | + l)) time [6], where l is the number of overlaps. Because we
only apply the scan-line algorithm after no more node overlaps are found along
edges of the proximity graph, l is usually a very small number, hence this step
can be considered as taking time O(|V | log |V |).
The proximity stress model (6), like the spring model (1), can be solved
62
Gansner and Hu Efficient Node Overlap Removal
using the stress majorization technique [13] which is known to be a robust
process for finding the minimum of (1). The technique works by bounding
(6) with a series of quadratic functions from above, and the process of finding
an optimum becomes that of finding the optimum of the series of quadratic
functions, which involves solving linear systems with a weighted Laplacian of the
proximity graph. We solve each linear system using a preconditioned conjugate
gradient algorithm. Because we use DT as our proximity graph and it has no
more than 3|V | − 6 edges, each iteration of the conjugate gradient algorithm
takes a time of O(|V |).
Overall, therefore, Algorithm 1 takes O(t(mk|V | + |V | log |V |)) time, where
t is the total number of iterations in the two main loops in Algorithm 1, m is
the average number of stress majorization iterations, and k the average number
of iterations for the conjugate gradient algorithm.
In practice, we found that the majority of CPU time is spent in repeatedly
solving the linear systems (which takes a total time of O(tmk|V |)). We terminate the conjugate gradient algorithm if the relative 2-norm residual for the
linear system involved in the stress majorization process is less than 0.01. A
tighter tolerance is not necessary because the solution of each linear system constitutes an intermediate step of the stress majorization. Furthermore, solution
of the proximity stress model (6) is an intermediate step itself in Algorithm 1,
so we do not need to solve (6) accurately either. Hence we set a limit of mmax
iterations. By experimentation, we found that a smaller value mmax gives a
faster algorithm, and that, in terms of quality, a smaller mmax is often just as
good as, if not better than, a larger value of mmax . Therefore, we set mmax = 1.
5
Numerical Results
To evaluate the PRISM algorithm and other overlap removal algorithms, we apply them as a post-processing step to a selection of graphs from the Graphviz [14]
test suite. This suite, part of the Graphviz source distribution, contains many
graphs from users. As such, these are good examples of the kind of graphs
actually being drawn.
Our baseline algorithm is Scalable Force Directed Placement (SFDP) [22], a
multilevel, spring-electrical algorithm. Using the layout of SFDP, we then apply
one of the overlap removal algorithms to get a new layout that has no node
overlaps, and compare the new layout with the original in terms of dissimilarity
and area.
In Table 1, we list the 14 test graphs, the number of vertices and edges, as
well as CPU time3 for PRISM and three other overlap removal algorithms. The
graphs are selected randomly with the criteria that a graph chosen should be
connected, and is of relatively large size. We compared PRISM with an implementation of the solve VPSC algorithm [6] provided by its authors. We also
evaluated the companion algorithm satisfy VPSC. This offered, at best, a 2%
3 All timings were derived on a 4 processor, 3.2 GHz Intel Xeon CPU, with 8.16 GB of
memory, running Linux.
JGAA, 14(1) 53–74 (2010)
63
Table 1: Comparing the CPU time (in seconds) of several overlap removal algorithms. Initially the layout is scaled to an average edge length of 1 inch.
Graph
b100
b102
b124
b143
badvoro
mode
ngk10 4
NaN
dpd
root
rowe
size
unix
xx
|V |
1463
302
79
135
1235
213
50
76
36
1054
43
47
41
302
|E|
5806
611
281
366
1616
269
100
121
108
1083
68
55
49
611
PRISM
1.44
0.14
0.03
0.04
0.54
0.09
0.01
0.01
0.01
0.89
0.00
0.01
0.01
0.13
VPSC
14.85
0.10
0.01
0.01
71.15
0.09
0.00
0.01
0.01
7.81
0.00
0.00
0.00
0.10
VORO
350.7
4.36
0.02
0.47
351.51
2.15
0.02
0.11
0.02
398.49
0.04
0.06
0.04
8.19
ODNLS
258.9
5.7
0.5
1.3
73.6
2.1
0.14
0.27
0.1
46.9
0.1
0.09
0.07
5.67
reduction in time, while producing almost identical results concerning displacement, dissimilarity and area. For this reason, in the sequel, we only consider
the solve VPSC algorithm, hereafter denoted as VPSC.4 We also evaluated the
Voronoi cluster busting algorithm [15, 29], denoted by VORO, as well as the
ODNLS algorithm of Li et al. [28], which relies on varied edge lengths in a spring
embedder. We note, in passing, that we also tested scaling using the algorithm
of Marriott et al. [30]. As expected, it outperformed all other algorithms in
terms of speed and dissimilarity, but at an unacceptably high cost in area. For
example, on the b143 graph, the time and dissimilarity were essentially 0 but
the area was 82.2. Overall, scaling produced areas at least 4.5 times larger than
PRISM and, more typically, at least an order of magnitude larger. We therefore
remove scaling from further consideration.
The initial layout by SFDP is scaled so that the average edge length is 1 inch.
From the table, it is seen that PRISM is usually faster, particularly for large
graphs on which it scales much better. The others are slow for large graphs,
with VORO the slowest.
Table 2 compares the dissimilarities and drawing area of the four overlap
removal algorithms. The smaller the dissimilarities and area, the better.
The ODNLS algorithm performs best in terms of smaller dissimilarity, followed by PRISM, VPSC and VORO. In terms of area, PRISM and VPSC are
pretty close, and both are better than ODNLS and VORO, which can give ex4 Both versions of the VPSC algorithm can be extended to support the preservation of
orthogonal ordering. We did not have an opportunity to check these versions.
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Gansner and Hu Efficient Node Overlap Removal
tremely large drawings. Indeed, in terms of area, scaling outperformed ODNLS
and VORO in 20%-30% of the examples.
Comparing PRISM with VPSC, Table 2 shows that PRISM gives smaller
dissimilarities most of the time. The two dissimilarity measures, σdist and σdisp ,
are generally correlated, except for ngk10 4 and root. Based on σdist , VPSC
is better for these two graphs, while based on σdisp , PRISM is better. The
first row in Figure 4 shows the original layout of ngk10 4, as well as the result
after applying PRISM and VPSC. Through visual inspection, we can see that
PRISM preserved the proximity relations of the original layout well. VPSC
“packed” the labels more tightly, but it tends to line up vertices horizontally
and vertically, and also produces a layout with aspect ratio quite different from
the original graph. It seems that σdist is not as sensitive in detecting differences
in aspect ratio. This is evident in drawings of the root graph (Figure 4, second
row): VPSC clearly produced a drawing that is overly stretched in the vertical
direction, but its σdist is actually smaller! Consequently, we conclude that σdisp
may be a better dissimilarity measure.
The fact that VPSC can produce very tall and thin, or very short and wide,
layouts is not surprising, and has been observed often in practice. VPSC works
in the vertical and horizontal directions alternatively, each time trying to remove
overlaps while minimizing displacement. As a result, when starting from a layout
with severe node overlaps, it may move vertices significantly along one direction
to resolve the overlaps, creating drawings with extreme aspect ratios. In fact,
for 9 out of 14 test graphs, VPSC produces layouts with extreme aspect ratios.
PRISM does not suffer from this problem.
When starting from a layout that is scaled sufficiently so that relative fewer
nodes overlap, VPSC’s performance can be improved. Table 3 compares the
four overlap removal algorithms, starting from layouts that are scaled to give
an average edge length that equals 4 times the average node size. Here the size
of a node is calculated as the average of its width and height.
From the table, we can see that in terms of dissimilarity, PRISM and VPSC
are now similar, closer to the better performing ODNLS. In terms of drawing
area, PRISM is better than VPSC, with VORO and ODNLS much larger. When
visually inspected, VPSC again suffers from extreme aspect ratio issue on at
least 5 out of the 14 graphs (b100, b143, badvoro, mode, root). Figure 5
shows the layout of badvoro (first row), on which VPSC performed badly based
on the two similarity measures. In the same figure, we also show b124 (second
row), on which PRISM is rated worse than VPSC based on the same measures.
On badvoro it is clear that VPSC performed badly, as the similarity measures
suggest. On the other hand, if we look at b124, VPSC perhaps performed better
than PRISM, but not as clearly as the similarity measures suggest. Overall,
visual inspection of the drawings of these 14 graphs, as well as drawings for
graphs in the complete Graphviz test suite (a total of 204 graphs in March
2008), shows that PRISM performs very well, and is overall better and faster
than VPSC and VORO. The ODNLS algorithm preserves similarity somewhat
better than PRISM, but at much higher costs in term of speed and area.
Considering a larger collection of graphs, Table 4 compares PRISM with
JGAA, 14(1) 53–74 (2010)
65
Table 2: Comparing the dissimilarities and area of overlap removal algorithms.
Results shown are σdist , σdisp and area. Area is measured with a unit of 106
square points. Initially the layout is scaled to an average length of 1 inch.
Graph
b100
b102
b124
b143
badvoro
mode
ngk10 4
NaN
dpd
root
rowe
size
unix
xx
Graph
b100
b102
b124
b143
badvoro
mode
ngk10 4
NaN
dpd
root
rowe
size
unix
xx
σdist
0.74
0.44
0.65
0.59
0.34
0.59
0.41
0.4
0.34
0.71
0.33
0.37
0.39
0.42
σdist
0.8
0.86
0.99
2.29
0.97
0.48
0.56
0.48
4.09
0.49
0.62
0.6
0.97
PRISM
σdisp
area
0.38
14.05
0.25
2.45
0.37
1.04
0.35
1.5
0.15
12.58
0.37
0.79
0.16
0.33
0.2
0.72
0.18
0.25
0.3
16.99
0.14
0.22
0.2
0.47
0.23
0.39
0.25
3.96
VORO
σdisp
area
0.3
31.79
0.39
13.42
0.45
22.91
0.65 3.01E3
0.54
10.84
0.26
0.52
0.28
5.04
0.32
0.45
0.94 6.93E9
0.26
0.95
0.35
1.27
0.35
0.85
0.34
58.83
σdist
0.76
0.58
0.78
0.78
0.61
1.02
0.39
0.54
0.51
0.6
0.44
0.77
0.51
0.57
σdist
0.33
0.30
0.33
0.49
0.31
0.38
0.22
0.26
0.37
0.29
0.27
0.32
0.26
0.29
VPSC
σdisp
area
0.72
18.91
0.8
2.71
0.73
0.91
0.83
2.16
0.75
13.85
0.77
1.29
0.3
0.25
0.65
0.71
0.4
0.18
0.75
17.68
0.31
0.19
0.74
0.4
0.67
0.36
0.82
3.9
ODNLS
σdisp
area
0.20 1.02E3
0.16
53.13
0.19
14.79
0.34
23.79
0.26 318.66
0.27
49.45
0.13
2.30
0.15
5.10
0.29
1.30
0.22 950.01
0.12
2.10
0.20
4.14
0.13
2.35
0.14
74.00
66
Gansner and Hu Efficient Node Overlap Removal
26
37
44
42
22
26
1
13
49
26
40
22
29
2 31 32
37
22
3
30
13
47
28
31
2
2
47
38
24
39
3
8
32
13
9
38
24
18
30
41
40
29
20
28
8
933
16 10
6
39 11
46
35 25
48
43
14
15
45
7 1250 19
27
34
17
4
36
21
5
23
47
38
42
44
1
44 42 3741
30
41
40
1
49
20
18
35
14
7
10
16
11
39
33
6
31
29
11
32
25
16
50
46
24
49
14
48
43
50
7
12
34
34
15
15
48
6
45
27
19
45
36
17
4
5
4
17
5
21
36
23
21
ngk10 4
33
19
27
23
3
9
10
20
43
12
46
25
35
18
28
8
ngk10 4+PRISM
ngk10 4+VPSC
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dca32af03698c988b22
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11bb8ed3ae227d3acefc
cd0d985a366cad7e
0f940646
f0bd1521
3b2f08d52e4bca3f9ca7bbbd6
6c632ad9c42228bb337
503737b64d432c60d6ac557e0e6
1d163eac141def176461c
f78e145a127014eb43345a0c
dca32af03698c988b22
18115fa32ff1cb99
84e4f1c582427a98d7b
ea890ccca2f7c2107351
18115fa32ff1cb99
fb039d7a2a9fe73b5f468eba9
0c72a426929600000f5
a27037332d9fa5c43bcfe94c0
0c72a426929600000f5
3cdc90c57243373efaba65a
173fd00917644f0f1f3e3
173fd00917644f0f1f3e3
24431c3eb075102f07cc2c1be
e3bdbca0e2256fffa8a59018
75ba8d840070942eb4e737849
07f8a9e55a16beddb3c9153b0
9c9e2e0f2da8758e436c
4a38abc630c82b0c48dfbf5271
86276bb1e23f2c7ffcbe82a0
root
root+PRISM
root+VPSC
Figure 4: Divergence of dissimilarity measures: for both graphs, σdist estimates
that VPSC gives layout closer to the original, while σdisp predicts the opposite.
hstntx72
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cmbrma75 cmbrma78
cmbrma70
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albyny60 hrfrct02
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clevoh67 bflony65
bflony64
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hrfrct71 hrfrct04
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chcgcg68
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badvoro
badvoro+PRISM
badvoro+VPSC
b124
b124+PRISM
b124+VPSC
F gure 5 Compar ng PRISM and VPSC on two graphs Or g na ayouts are
sca ed to have an average edge ength that equa s 4 t mes the abe s ze
JGAA, 14(1) 53–74 (2010)
67
Table 3: Comparing the dissimilarities and area of overlap removal algorithms.
Results shown are σdist , σdisp and area. Area is measured with a unit of 106
square points. Initially the layout is scaled to an average edge length that equals
4 times the average label size.
Graph
b100
b102
b124
b143
badvoro
mode
ngk10 4
NaN
dpd
root
rowe
size
unix
xx
Graph
b100
b102
b124
b143
badvoro
mode
ngk10 4
NaN
dpd
root
rowe
size
unix
xx
σdist
0.74
0.41
0.52
0.5
0.35
0.57
0.25
0.25
0.14
0.73
0.16
0.35
0.25
0.39
σdist
1.18
0.69
0.84
3.8
1.09
0.46
0.49
0.43
4.14
0.41
0.62
0.55
1.13
PRISM
σdisp
area
0.36
14.59
0.18
2.62
0.12
3.39
0.22
2.59
0.15
11.85
0.35
0.78
0.05
0.54
0.06
1.15
0.03
0.54
0.28
16.02
0.04
0.38
0.11
0.54
0.07
0.6
0.18
4.23
VORO
σdisp
area
0.47 131.55
0.36
19.09
0.39
19.35
0.9
4.45E5
0.58
20.02
0.2
0.79
0.22
2.28
0.23
0.6
0.94 3.68E8
0.2
0.68
0.34
2.07
0.24
0.64
0.44
185.7
σdist
0.95
0.44
0.28
0.67
0.65
0.84
0.16
0.15
0.1
0.73
0.11
0.28
0.13
0.45
σdist
0.49
0.33
0.43
0.57
0.34
0.44
0.23
0.33
0.38
0.39
0.25
0.28
0.20
0.30
VPSC
σdisp
area
0.62
25.33
0.33
2.77
0.06
3.04
0.41
4.26
0.58
11.71
0.59
1.45
0.03
0.53
0.04
1.15
0.03
0.53
0.7
25.93
0.03
0.38
0.08
0.57
0.04
0.59
0.34
4.54
ODNLS
σdisp
area
0.24 1.09E3
0.15
41.01
0.26
14.64
0.36
29.39
0.10 166.53
0.28
45.21
0.12
2.21
0.18
4.86
0.29
1.45
0.14 1.52E3
0.11
2.01
0.16
3.35
0.09
2.01
0.11
45.18
68
Gansner and Hu Efficient Node Overlap Removal
Table 4: Comparing dissimilarity and area of overlap removal algorithms on the
Rome suite of test graphs. # stands for the number of graphs within the size
range specified.
sizes
#
10–19
20–29
30–39
40–49
50–59
60–69
70–79
80–89
90–99
100–109
1407
839
2036
1800
1045
1172
1008
788
1296
140
PRISM
σdisp area
0.009 0.16
0.02 0.27
0.03 0.36
0.035 0.43
0.042 0.51
0.046 0.58
0.051 0.64
0.05 0.71
0.054 0.78
0.055 0.82
VPSC
σdisp area
0.09 0.061
0.11
0.12
0.13
0.19
0.14
0.25
0.15
0.32
0.17
0.39
0.17
0.46
0.17
0.52
0.18
0.59
0.18
0.61
VORO
σdisp area
0.14 0.069
0.14
0.15
0.13
0.26
0.12
0.36
0.11
0.53
0.11
0.70
0.11
0.94
0.10
1.20
0.10
1.49
0.10
1.7
ODNLS
σdisp
area
0.07
0.34
0.078 0.92
0.078 1.85
0.074 2.71
0.074 4.53
0.074 6.18
0.073 8.44
0.07
9.99
0.069 13.26
0.068 14.14
VPSC, VORO and ODNLS on the Rome test suite of graphs [4]. This suite has
a total of 11534 graphs5 of relatively small size. Due to space limitation, we only
give the similarity measure σdisp and the area, and we average the results over
graphs of similar sizes. Again, PRISM achieves the best compromise between
being close to the original drawing, and having a smaller drawing area.
We note that while there is no theoretical result guaranteeing that PRISM
algorithm converges to an overlap free layout in a finite number of iterations, in
practice, out of thousands of graphs tested, some as large as tens of thousands
of vertices, PRISM always converges within a few hundred total number of
iterations in the two main loops in Algorithm 1. In our implementation we set
a limit of 1000 iterations, even though this limit has never been observed to be
reached. Table 5 gives the number of iterations taken for the 14 test cases in
Tables 2-3. As can be seen, for these graphs, the maximum number of iterations
is 122.
As a demonstration of the scalability of PRISM, we consider its application
to a large graph. This is a tree from the Mathematics Genealogy Project [32].
Each node is a mathematician, and an edge from node i to node j means that j
is the first supervisor of i. The graph is disconnected and consists of thousands
of components. Here we consider the second largest component with 11766
vertices. This graph took 31 seconds to lay out using SFDP, and 15 seconds
post-processing using PRISM for overlap removal. PRISM converges in 81 iterations. Important mathematicians (those with the most offspring) and important
edges (those that lead to the largest subtrees) are highlighted with larger nodes
5 Three
graphs were dropped from the test because they were disconnected.
JGAA, 14(1) 53–74 (2010)
69
Table 5: Number of iterations taken in the two main loops in Algorithm 1. A:
initially the layout is scaled to an average edge length of 1 inch. B: initially the
layout is scaled to an average edge length that equals 4 times the average label
size.
Graph
b100
b102
b124
b143
badvoro
mode
ngk10 4
NaN
dpd
root
rowe
size
unix
xx
|V |
1463
302
79
135
1235
213
50
76
36
1054
43
47
41
302
|E|
5806
611
281
366
1616
269
100
121
108
1083
68
55
49
611
A
122
66
43
46
53
43
29
34
26
103
28
29
32
53
B
75
44
19
26
32
26
8
9
6
119
7
14
8
46
and thicker edges. Figure 6(top) gives the overall layout, which shows that
PRISM preserved the tree structure of the layout very well after node overlap
removal. Figure 6(bottom) gives a close up view of the details of a small area in
the center-left part of Figure 6(top) with many famous mathematicians of early
generations. Additional drawings of this and other components of the Mathematics Genealogy Project graph, including that of the largest component, are
available [21].
6
Conclusions and Future Work
A number of algorithms have been proposed for removing node overlaps in
undirected graph drawings. For graphs that are relatively large with nontrivial
connectivities, these algorithms often fail to produce satisfactory results, either
because the resulting drawing is too large (e.g., scaling, VORO, ODNLS), or
the drawing becomes highly skewed (e.g., VPSC). In addition, many of them
do not scale well with the size of the graph in terms of computational costs.
The main contributions of this paper is a new algorithm for removing overlaps
that is both highly effective and efficient. The algorithm is shown to produce
layouts that preserve the proximity relations between vertices, and scales well
with the size of the graph. It has been applied to graphs of tens of thousands of
vertices, and is able to give aesthetic, overlap-free drawings with compact area
70
Gansner and Hu Efficient Node Overlap Removal
in seconds, which is not feasible with any algorithm known to us.
It is possible that algorithms such as VPSC, which rely on separate passes in
the X and Y directions, might be improved by randomizing which overlaps are
removed in which pass or by gradually removing overlaps using many alternating
X and Y passes. This would, however, further increase their computational cost,
which is already much higher than the algorithm proposed in this paper.
For future work, we would like to extend the overlap removal algorithm to
deal with edge-node overlaps. We would also like to explore the possibility of
using the proximity stress model for packing disconnected components.
Acknowledgments
We would like to thank Tim Dwyer and Wanchun Li for making their implementations of VPSC and ODNLS, respectively, available to us. We would like
to thank Yehuda Koren and Stephen North for helpful discussions, and Stephen
Kobourov for bringing our attention to the term “Frobenius metric”. Finally,
the reviewers’ comments were very helpful, especially in making the exposition
clearer and more accurate.
JGAA, 14(1) 53–74 (2010)
71
Karagrigoriou
Winnicki
Guo
Lee
Feng
Chan
Bendsøe
Park
Chan
Rabinowitz
Yu
Wang
Nielsen
Sigal
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N w
F gure 6 The second argest component from the Mathemat cs Genea ogy
Project Top overa ayout w th node over ap removed Bottom c ose up
v ew of a sma area of the center- eft part of above
72
Gansner and Hu Efficient Node Overlap Removal
References
[1] I. Borg and P. Groenen. Modern Multidimensional Scaling: Theory and
Applications. Springer, 1997.
[2] U. Brandes and C. Pich. An experimental study on distance based graph
drawing. In GD’08: Proceedings of the Symposium on Graph Drawing, 2008
(to appear).
[3] J.-H. Chuang, C.-C. Lin, and H.-C. Yen. Drawing graphs with nonuniform
nodes using potential fields. In Proc. 11th Intl. Symp. on Graph Drawing,
volume 2012 of LNCS, pages 460–465. Springer-Verlag, 2003.
[4] G. Di Battista, A. Garg, G. Liotta, R. Tamassia, E. Tassinari, and
F. Vargiu. An experimental comparison of four graph drawing algorithms.
CGTA: Computational Geometry: Theory and Applications, 7:303–325,
1997.
[5] T. Dwyer, Y. Koren, and K. Marriott. Ipsep-cola: An incremental procedure for separation constraint layout of graphs. IEEE Transactions on
Visualization and Computer Graphics, 12(5):821–828, 2006.
[6] T. Dwyer, K. Marriott, and P. J. Stuckey. Fast node overlap removal. In
Proc. 13th Intl. Symp. Graph Drawing (GD ’05), volume 3843 of LNCS,
pages 153–164. Springer, 2006.
[7] P. Eades. A heuristic for graph drawing. Congressus Numerantium, 42:149–
160, 1984.
[8] H. Edelsbrunner and E. P. Mücke. Three-dimensional alpha shapes. ACM
Trans. on Graphics, 13(1):43–72, 1994.
[9] C. Erten, A. Efrat, D. Forrester, A. Iyer, and S. G. Kobourov. Forcedirected approaches to sensor network localization.
In R. Raman,
R. Sedgewick, and M. F. Stallmann, editors, Proc. 8th Workshop Algorithm
Engineering and Experiments (ALENEX), pages 108–118. SIAM, 2006.
[10] S. Fortune. A sweepline algorithm for Voronoi diagrams. Algorithmica,
2:153–174, 1987.
[11] C. Friedrich and F. Schreiber. Flexible layering in hierarchical drawings
with nodes of arbitrary size. In Proceedings of the 27th conference on Australasian computer science (ACSC2004), pages 369–376. Australian Computer Society, 2004.
[12] T. M. J. Fruchterman and E. M. Reingold. Graph drawing by force directed
placement. Software - Practice and Experience, 21:1129–1164, 1991.
[13] E. R. Gansner, Y. Koren, and S. C. North. Graph drawing by stress majorization. In Proc. 12th Intl. Symp. Graph Drawing (GD ’04), volume 3383
of LNCS, pages 239–250. Springer, 2004.
JGAA, 14(1) 53–74 (2010)
73
[14] E. R. Gansner and S. North. An open graph visualization system and its
applications to software engineering. Software - Practice & Experience,
30:1203–1233, 2000.
[15] E. R. Gansner and S. C. North. Improved force-directed layouts. In Proc.
6th Intl. Symp. Graph Drawing (GD ’98), volume 1547 of LNCS, pages
364–373. Springer, 1998.
[16] J. C. Gower and G. B. Dijksterhuis. Procrustes Problems. Oxford University
Press, 2004.
[17] L. Guibas and J. Stolfi. Primitives for the manipulation of general subdivisions and the computation of voronoi. ACM Trans. Graph., 4(2):74–123,
1985.
[18] S. Hachul and M. Jünger. Drawing large graphs with a potential field based
multilevel algorithm. In Proc. 12th Intl. Symp. Graph Drawing (GD ’04),
volume 3383 of LNCS, pages 285–295. Springer, 2004.
[19] D. Harel and Y. Koren. A fast multi-scale method for drawing large graphs.
J. Graph Algorithms and Applications, 6:179–202, 2002.
[20] K. Hayashi, M. Inoue, T. Masuzawa, and H. Fujiwara. A layout adjustment
problem for disjoint rectangles preserving orthogonal order. In Proc. 6th
Intl. Symp. Graph Drawing (GD ’98), volume 1547 of LNCS, pages 183–
197. Springer, 1998.
[21] Y. F. Hu. Drawings of the mathematics genealogy project graphs.
http://www.research.att.com/˜yifanhu/GALLERY/MATH GENEALOGY.
[22] Y. F. Hu. Efficient and high quality force-directed graph drawing. Mathematica Journal, 10:37–71, 2005.
[23] Y. F. Hu and Y. Koren. Extending the spring-electrical model to overcome
warping effects. In Proceedings of IEEE Pacific Visualization Symposium
2009 (PacificVis ’09), pages 129–136, 2009.
[24] X. Huang and W. Lai. Force-transfer: A new approach to removing overlapping nodes in graph layout. In Proc. 25th Australian Computer Science
Conference, pages 349–358, 2003.
[25] J. W. Jaromczyk and G. T. Toussaint. Relative neighborhood graphs and
their relatives. Proc. IEEE, 80:1502–1517, 1992.
[26] T. Kamada and S. Kawai. An algorithm for drawing general undirected
graphs. Information Processing Letters, 31:7–15, 1989.
[27] G. Leach. Improving worst-case optimal Delaunay triangulation algorithms.
In 4th Canadian Conference on Computational Geometry, pages 340–346,
1992.
74
Gansner and Hu Efficient Node Overlap Removal
[28] W. Li, P. Eades, and N. Nikolov. Using spring algorithms to remove node
overlapping. In Proc. Asia-Pacific Symp. on Information Visualisation,
pages 131–140, 2005.
[29] K. A. Lyons, H. Meijer, and D. Rappaport. Algorithms for cluster busting
in anchored graph drawing. J. Graph Algorithms and Applications, 2(1),
1998.
[30] K. Marriott, P. J. Stuckey, V. Tam, and W. He. Removing node overlapping
in graph layout using constrained optimization. Constraints, 8(2):143–171,
2003.
[31] K. Misue, P. Eades, W. Lai, and K. Sugiyama. Layout adjustment and the
mental map. J. Vis. Lang. Comput., 6(2):183–210, 1995.
[32] North Dakota State University Dept. of Math. The mathematics genealogy
project.
http://genealogy.math.ndsu.nodak.edu/.
[33] J. R. Shewchuk. Engineering a 2D quality mesh generator and Delaunay
triangulator. In Applied Computational Geometry: Towards Geometric
Engineering, volume 1148 of LNCS, pages 203–222. Springer, 1996.
[34] J. R. Shewchuk. Delaunay refinement algorithms for triangular mesh generation. Computational Geometry: Theory and Applications, 22:21–74, 2002.
[35] K. Sugiyama, S. Tagawa, and M. Toda. Methods for visual understanding
of hierarchical systems. IEEE Trans. Systems, Man and Cybernetics, SMC11(2):109–125, 1981.
[36] C. Walshaw. A multilevel algorithm for force-directed graph drawing. J.
Graph Algorithms and Applications, 7:253–285, 2003.
[37] X. Wang and I. Miyamoto. Generating customized layouts. In GD ’95:
Proceedings of the Symposium on Graph Drawing, volume 1027 of LNCS,
pages 504–515. Springer, 1995.