MATH 884 Presentation:

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MATH 884 Presentation Dynamic Routing in a
Linear Multi-Waveband Optical Network Present
ed by Andrew Gibson
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1
1
C
A
F
B
G
2
H
E
D
3
2
3
Example of an optical network.
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• Properties of Linear Optical Networks
• Linear operations vs. non-linear operations
• Graph Construction
• LDCs
• Wavebands
• Assumptions

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Optical Spectrum
Channel 2
Channel 2
Channel 1
Channel 1
Waveband 1
Waveband 2
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• Restrictions on Linear Optical Networks
• Channel Continuity
• Distinct Channel Assignment
• Inseparability (VERY IMPORTANT CONCEPT)
• Mutually Independent Sources Combining (MISC)
• Color Clash

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1
1
C
S1
S1
S1
S1
S1
S1
A
F
B
G
2
H
E
D
3
2
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Now add path (2,2) 2-A-B-D-E-2 on the same
waveband as (1,1) but a different channel (dont
violate Distinct Waveband-Channel
Assignment) Note this is the min-hop path
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1
1
C
S1S2
S1
S1S2
S1S2
S1S2
A
F
B
G
S1S2
S1S2
S2
2
H
E
D
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S1S2
S1S2
2
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This unintended multicasting is a result of
inseparability. Note S1 and S2 are interfering
signals.
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• Where are we now?
• Intro to Linear Optical Networks
• Properties of Linear Optical Networks - DONE
• Restrictions within Linear Optical Networks -
  DONE
• Where next?
• Introduce and decompose routing problem
• Waveband selection
• Path selection
• Conclusions

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• Routing Problem
• Choose a Waveband for the incoming call
• Finding a Path within a selected Waveband
• Checking for violations of network constraints
• Assigning the Channel or blocking the signal.

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• Choose a Waveband for a selected call
• Two different rules for choosing a Waveband
  MAXBAND and MINBAND
• Let (Wb1, .. , Wbk) be the k different wavebands
  on the links

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Finding a Path within a selected
Waveband Theorem 1 Finding a path, within a
chosen Waveband, form a
source transmitter s to destination receiver t
that satisfies the MISC constraint on it
as well as all associated unintended
paths due to inseparability is
NP-Complete. Theorem 2 A polynomial time
algorithm exists which can find a path from
a source s to a destination t, within a chosen
Waveband that satisfies the Color Clash
constraint on it as well as all associated
unintended paths.
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• Finding a Path within a selected waveband
• Min-Int
• Definitions
• An internodal link from node i to node j will be
  denoted by (i,j) and it can be assigned any
  weight as with the K-SP algorithm
• An intranodal link inside node k joining inbound
  link (i,k) and (k,j) will be assigned a weight
• Ik(i,j) M G(k , j) G(i , k)
• Where G(k , j ) the set of signals carried
  on link ( k , j)
• Complexity O ( m log(n))
• Where m is the number of links in the network
  and n is the number of nodes

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Checking for violations of network
constraints Recursive algorithm with complexity
of O(m)
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• Assigning the Channel or blocking the signal
• If a path can be provided then a Channel within
  the selected waveband must be used.
• The same algorithm for selecting wavebands is
  used for selecting the individual Channels.

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Conclusions One algorithm has been proposed for
accomplishing the task of dynamic routing within
a linear optical network. The worst case
complexity is O(k m m log(n))