Information Technology Reference
In-Depth Information
to get the assignment sets
Α
(λ
,
Α
(λ
,
⋅⋅⋅
,
Α
()
λ
for the channels at
λ
,
λ
,
⋅⋅⋅
,
λ
respectively.
Step 3. Channel Assignment
We remove the dummy items added in step 1 from the corresponding ones in
Α
(λ
,
,
⋅⋅⋅
,
Α
(λ
Α
()
λ
λ
based on
Α
()
λ
. Then we perform channel assignment at
for all
1
≤≤
as follows: for every
(, )
kW
iz
∈Α
(
λ
)
λ
to
, assign a wavelength channel at
i
k
connect demultiplexer
i
to passive combiner
z
.
In the above channel assignment method, the most time-consuming step is to solve a
sequence of
W
distinct representative problems. Each of these problems can be solved in
3
OM
(
)
steps [26]. Therefore, our channel assignment method has a time complexity of
3
OWM
(
)
.
4.3. Numerical Example
We consider a multi-passive-combiner hub with four nodes and the following channel
requirement matrix:
0316
2017
1202
7530
⎡
⎤
(6)
⎢
⎥
⎢
⎥
D
=
⎢
⎥
⎢
⎥
⎣
⎦
W
=
. After executing step 1 of the channel assignment method, the channel
requirement matrix
D
is transformed to the following representation:
5
Let
00301100
00000410
20001020
00000023
10200002
23000000
02030000
00023000
⎡
⎤
⎢
⎥
⎢
⎥
⎢
⎥
(7)
⎢
⎥
⎢
⎥
D
′ =
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎣
⎦
Correspondingly, the four nodes have 2, 2, 1, 3 fibers to the hub respectively and 2, 2, 1,
3 fibers from the hub respectively. After executing steps 2 and 3, we get the following
assignment sets:
Α=
(
)
{(1,5),(2,6),(3,7),(4,8),(5,3),(6,1),(7,2),(8,4)}
1
Α=
(
)
{(1,3),(2,6),(3,7),(4,8),(5,1),(6,2),(7,4),(8,5)}
2
(8)
Α=
(
)
{(1, 3), (2, 6), (3, 5), (4, 7), (5, 8), (6,1), (7, 2), (8, 4)}
3