Information Technology Reference
In-Depth Information
t
t
p
p
3
3
1
p
4
p
t
p
5
p
'
5
8
p
6
t
p
6
9
t
p
t
2
2
4
p
7
Web service provided
Web service component
Dummy Web service
Figure 5.3
SC-net representation of the configuration of system A.
In order to derive the candidate Web service configurations automat-
ically and obtain a more efficient QoS search algorithm, in this section,
we analyze the graph and the algebraic structural properties of the SC-net.
5.3.2 Definition of Incidence Matrix and
State-Shift Equation
Definition 5.7.
For an SC-net with m places and n transitions, following
[80], the incidence matrix A
¼½
a ij
¼
W
ð
t j
;
p i Þ
- W
ð
p i ;
t j
Þ
is an m
n
matrix of integers.
For example, for the SC-net in Figure 5.3, the incidence matrix
2
4
3
5
T
1
;
1
;
0
;
0
;
0
;
0
;
0
;
0
;
0
;
0
1
;
0
;
1
;
0
;
0
;
0
;
0
;
0
;
0
;
0
0
0
0 ; 0 ; 1 ; 0 ; 0 ; 1 ; 1 ; 1 ; 0 ; 0
0
;
1
;
0
;
1
;
1
;
0
;
0
;
0
;
0
;
A
¼
:
;
;
;
;
;
;
;
;
;
0
0
0
0
0
1
0
1
0
0
;
0
;
0
;
0
;
0
;
0
;
1
;
0
;
0
;
1
Definition 5.8.
The state-shift equation is E - A
½
a ¼
M 0 , where A is
is an
M
x
the incidence matrix,
a ¼
ð
m
þ
n
Þ
1 column vector, and
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