Information Technology Reference
In-Depth Information
*
2
m
1
RAAA A
RRR
Tt
...
i
i
i
i
i
k
1
k
k
[]
:
t k mr
{min
[1, s .
0}
i
m
m
i
i
Precalculate offline
T
matrix
Reach. matrix
Adj. matrix
Workflows
w
A
R
1
1
1
w
A
R
2
2
2
R
T
w
A
R
n
n
n
Get result online
Figure 8.15
Obtain the least transfer route between two operations.
W
i
in which
O
i
is the set of (service) operations in
W
i
and
E
i
is the set of edges among these operations.
A
i
¼ð
O
i
;
E
i
Þ
:
O
i
O
i
!f
0
;
1
g
is the
adjacent matrix
of
W
i
. That is, given
o
ik
;
o
ij
2
O
i
, element
½
k
;
j
of
A
i
is defined as
A
ikj
¼
1if
o
ik
has a link to
o
ij
in
W
i
and 0 otherwise.
A
i
can be directly obtained from
W
i
. Based on the adjacent matrix,
we can derive the reachability matrix of each workflow.
Step 2: Calculate a Reachability Matrix.
R
i
:
O
i
O
i
!f
0
;
1
g
is the
reachability matrix
of
W
i
.
Given
o
ik
;
o
ij
2
O
i
, element
½
k
;
j
of
R
i
is defined as
R
ikj
¼
1if
o
ik
can
reach
o
ij
in
W
i
and 0 otherwise.
R
i
cannot be directly obtained from
W
i
. Instead, it can be calculated
from matrix
A
i
:
A
i
¼
A
i
þþ
A
m
i
1
A
i
þ
(
m
i
is the dimension of
A
i
)
i
1if
A
ikj
>
0
0 otherwise
R
ikj
¼
