Information Technology Reference
In-Depth Information
To return to
G
, the clusters' dimensions, i. e., their rectangular bounding
boxes, are applied to the compound nodes in
V
A
.Theedgesin
H
are split into
segments
s
1
,...,s
n
based on the crossing points
c
i
with clusters. The route of
s
i
is applied to the corresponding edge
e
\
∈
E
and the
c
i
determine the positions
of the hierarchical ports.
4 Evaluation and Discussion
We evaluate our approach on a set of data flow diagrams that ship with the
Ptolemy project
1
, comparing with the KLay Layered algorithm of Schulze et al.
Diagrams were chosen to be roughly the size Klauske found to be typical for
real-world Simulink models from the automotive industry [11] (about 20 nodes
and 30 edges per hierarchy level).
Metrics.
Well established metrics to assess the quality of a drawing are
edge
crossings
and
edge bends
[14], two metrics directly optimized by the layer-based
approach. More recently,
stress
and
edge length variance
were found to have a
significant impact on the readability of a drawing [4]. Additionally, we regard
compactness in terms of
aspect ratio
and
area
.
So that comparisons of edge length and of layout area can be meaningful, we
set the same value for KLay Layered's inter-layer distance and CoDaFlow's ideal
separation between nodes.
The
P
-stress of a given (already layouted) diagram depends on the choice
of the ideal edge length
in (1), and the canonical choice
¯
is that where the
function takes its global minimum. If
L
is a list of all the individual ideal lengths
uv
=
b
(
u,v
)
/p
uv
,then
¯
is equal to the
contraharmonic mean C
(
L
j
)(i.e.,the
weighted arithmetic mean in which the weights equal the values) over a certain
sublist
L
j
ↆ
L
.Namely,if
L
E
=
uv
:(
u,v
)
∈
E
and
L
\
L
E
=
1
≤
2
≤···≤
ʽ
ʽ
.Since
ʽ
is finite, we can
compute each
C
(
L
j
)andtake
¯
to be that at which the
P
-stress is minimized,
cf. [15].
,then
L
j
=
L
E
∪
1
,
2
,...,
j
for some 0
≤
j
≤
Results.
Table 1 and 2 show detailed results for layouts created by CoDaFlow
and KLay Layered. We used two variations of the Ptolemy diagrams: small flat
diagrams and compound diagrams (cf. [15] for further examples).
For flat diagrams CoDaFlow shows a better performance on stress, average
edge length, and variance in edge length. CoDaFlow produced slightly more
crossings, bends per edge, and slightly increased area.
More interesting are the results for the compound diagrams, which show more
significant improvements. On average, CoDaFlow's diagram area was 88% that
of KLay Layered, and edge length variance was only 29%. Also, the average
aspect ratio shifts closer to that of monitors and sheets of paper. However, there
is an increase in crossings. Currently our approach does not consider crossings
