Information Technology Reference
In-Depth Information
The combined DAGMap and node-link visualization provide an efficient ex-
ploratory device in order to develop an overview of these phenomena. Figure
7.1
b
shows the DAGMap view of subsidiaries in the car industry for the Fiat international
group. Cells have been colored according to whether subsidiaries are in Europe
(blue to dark blue is used to indicate that a company belongs to one of the
15 founding European countries), Asia (yellow), North America (orange), South
America (green) or Africa (gray). This color coding was designed with the help of
geographers. The geographers assigned a special color code for subsidiaries that
are suspected tax havens (magenta). The DAGMap relies on a squarified treemap
algorithm (
Bruls et al.
,
2000
), where the cell size corresponds to the amount of
company assets.
The DAGMap does not simply encode a tree but actually encodes a DAG.
This translates into being able to determine, in the treemap itself, if a subsidiary
depends on a single ancestor company or is held by more than one of the competing
companies. By clicking on a cell, the user can readily see whether the underlying
element encompasses other cells in the treemap. This visual feedback provides a
quick measure of the presence of a subsidiary in the network and aids with analyzing
company strategies. This is the case for the subsidiary “Centro Studi sui Sistemi di
Trasporto” (CSST for short), which depends on both “Iveco S.p.A.” and “Fiat Auto
Holdings B.V.” Examining the node link diagram, we indeed see that CSST sits
between these two companies. Moreover, we observe that “Fiat Auto Holdings B.V.”
does not hold its CSST subsidiary directly but rather through “Fiat Auto S.p.A.”.
We do not wish to draw any conclusions about the relationships between these
companies and their subsidiaries. We rather wish to draw attention to the utility of
this combined view, as was reported to us during our interviews with geographers.
7.4
DAGMaps: Extending TreeMaps to Directed
Acyclic Graphs (DAGS)
Treemaps appear to be an excellent alternative to the traditional (node-link) layout
for trees (
Shneiderman
,
1992
), emphasizing the attributes of leaf nodes as opposed
to the relative position of nodes in the tree. The DAGMap we describe here aims to
dothesameforDAGs.
We now explain how to adapt the basic TreeMap algorithm to address DAGs.
Roughly speaking, the DAG is unfolded into a tree by duplicating nodes wherever
necessary. Thus, a node
v
with multiple parents is duplicated as many times as
necessary so that each parent has its own copy of
v
. In formal terms, let
G
=(
V
,
E
)
be a DAG. Given a node
v
∈
V
,let
F
(
v
)
denote the parents of
v
in
G
.Inother
words,
F
(
v
)=
{
u
∈
V
|
(
u
,
v
)
∈
E
}
. Now, assume that the subgraph
H
induced by
the set of descendant nodes of
v
V
(nodes accessible by going downwards from
v
, including
v
itself) is a
tree
. For each parent
u
∈
∈
F
(
v
)
, we clone the subtree
H
and attach it below
u
. In doing so, the nodes
u
now have distinct
descendants (as far as
v
is concerned) (see Fig.
7.8
). Performing this transformation
∈
F
(
v
)
Search WWH ::
Custom Search