Information Technology Reference
In-Depth Information
industrial buildings are typical places where asbestos found widespread application,
since the invention of the mixture of cement and asbestos known as Eternit at the
beginning of the last century. When in the second half of the century it became clear
that asbestos can be very noxious to the human health, it became relevant to remove it
from buildings containing it.
Now let us suppose that later on this community evolves by merging with another
community for which the concept “Asbestos Removal” cannot by itself (on the basis
of its training) classify properly. By our procedure, this automatically identifies a
self-trained concept which we baptize (based on our own internalization of this com-
munity) “PV Integration”, referring to the integration of photovoltaic modules in
buildings so as to make them capable to produce, from the solar light, electricity to be
consumed by the residential units in the buildings. For obvious reasons of exposure to
light, roofs are indeed the most natural candidates for such an integration. We then
add a super-concept which can be viewed as an abstraction of the merging of the two
communities, and can be properly named “Asbestos Removal and PV-Integration”,
meaning that whenever we remove asbestos from a roof, we can as well kill two pi-
geons with one stone by replacing the asbestos parts with PV modules so as to make
the building not only environmentally safe but also “clean and green” from the stand-
point of energy production. The emergence of this concept is indeed at the basis of the
integration, as is currently taking place, between the asbestos removal industry an the
engineering of roof-based PV power plants.
The method for the discovery of Web communities is based upon the following re-
sult due to Ford and Fulkerson ([8]). We call s-t graph a structure of the form
(
V
,
E
,
s
,
t
).
Theorem 1.
Let G
= (
V,E
,
s
,
t
)
be an s-t graph. Then the maximum flow is equal to the
minimum s-t cut.
A
minimum cut
is a cut which minimizes the total capacities of the cut edges and the
following theorem, due to Ford and Fulkerson, states that the maximum graph flow
equals to the value of a minimum cut.
Theorem 2.
Let G
=(
V
,
E
)
be a graph. Then a community C
can be identified by calcu-
lating the s-t minimum cut with s and t being used as the source and sink respectively.
We then have the following algorithm of community extraction found by Flakes,
Lawrence and Gilles.([7]). Suppose
T
=
V
\
S
for a subset
S
⊆
V
. If
s
∈
S, t
∈
T
then the
edge set {(
u
,
v
)
T
} is called a
s-t cut
(or cut) on a graph
G
, and an edge
included in the cut set is called a
cut edge
.
∈
E
|
u
∈
S
,
v
∈
The procedure is as follows:
1.
S
is a set of seed nodes and
G
= (
V
,
E
) is a subgraph of the Web graph crawled
within a certain depth from the nodes in
S
, i.e. certain in/out links away from the
nodes in
S
. The subgraph
G
is called
vicinity graph
.
2. Suppose that any edge
e
E
is undirected with edge capacity
c
(
e
) =|
S
|.
3. Add a virtual source node
s
to
V
with the edge connecting to all nodes in
S
with
edge capacity =
∈
and finally add a virtual sink node
t
to
V
with the edges connected
from all the nodes in
V
-{
S
∞
∪
{
s
}
∪
{
t
}} with the edge capacity = 1.
4.
Then perform the
s
-
t
maximum flow algorithm for
G
.
