Wavelength Assignment in Optical Network Design

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Wavelength Assignment in Optical Network Design

• Team 6 Lisa Zhang (Mentor)
• Brendan Farrell, Yi Huang, Mark Iwen,
• Ting Wang, Jintong Zheng
• Progress Report
• Presenters Mark Iwen

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Wavelength Assignment

• Motivated by WDM (wavelength division
  multiplexing) network optimization
• Input
• A network G(V,E)
• A set of demands with specified src, dest and
  routes
• demand di (si, ti, Ri)
• WDM fibers
• U fiber capacity, number of wavelengths per
  fiber
• Output
• Assign a wavelength for each demand route
• Demand paths sharing same fiber have distinct
  wavelengths

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Example
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Model 1 Min conversion
Fiber capacity u 2 Demand routes AOB, BOC, COA

• Routes given
• L(e) load on link e
• u fiber capacity
• f(e) ? L(e) / u ?
• Deploy f(e) fibers on link e no extra fibers
• Use converters if necessary
• Min number of converters

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Model 1 Min conversion
Model 2 Min fiber

• Routes given
• L(e) load on link e
• u fiber capacity
• f(e) ? L(e) / u ?
• Deploy f(e) fibers on link e no extra fibers
• Use converters if necessary
• Min number of converters

• Each demand path assigned one wavelength from src
  to dest no conversion
• Deploy extra fibers if necessary
• Min total fibers

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Model 1 Min conversion
Model 2 Min fiber

• Routes given
• L(e) load on link e
• u fiber capacity
• f(e) ? L(e) / u ?
• Deploy f(e) fibers on link e no extra fibers
• Use converters if necessary
• Min number of converters

• Each demand path assigned one wavelength from src
  to dest no conversion
• Deploy extra fibers if necessary
• Min total fibers

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Complexity

• Perspective of worst-case analysis
• NP hard
• Cannot expect to find optimal solution
  efficiently for all instances
• Hard to approximate
• Cannot approximate within any constant
  AndrewsZhang
• For any algorithm, there exist instances for
  which the algo returns a solution more than any
  constant factor larger than the optimal.

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Heuristics

• Focus
• Simple/flexible/scalable heuristics
• Typical input instances not worst-case
  analysis
• A greedy heuristic
• For every demand d in an ordered demand set
• Choose a locally optimal solution for d

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Why greedy?

• Viable approach for many hard problems
• Set Cover Problem (NP-hard)
• SAT solving (NP-hard)
• Planning Problems (PSPACE-hard)
• Vertex Coloring (NP-hard)

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Vertex coloring A closely related problem

• A classic problem from combinatorial optimization
  and graph theory
• Problem statement
• Graph D
• Color each vertex of D such that neighboring
  vertices have distinct colors
• Minimize the total number of colors needed

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Connection to vertex coloring

• Create a demand graph D from wavelength
  assignment instance G
• One vertex for each demand
• Two demands vertices adjacent iff demand routes
  share common link
• Demand graph D is u colorable iff wavelength
  assignment feasible with 0 extra fibers and 0
  conversion.

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What we know about vertex coloring

• Complexity worst case
• NP-hard
• Hard to approximate cannot be approximated to
  within a factor of n1-e FeigeKilianKnotPonnusw
  ami
• Heuristic solutions common cases
• Greedy approaches extremely effective
• For vertex v in an ordering of vertices
• Color v with smallest color not used by vs
  neighbors
• Example Brelazs algorithm Turner gives
  priority tomost constrained vertex

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Try greedy wavelength assignment
For every demand d in an ordered demand set
Choose a locally optimal solution for d - Is
there good ordering? - Is it easy to find a good
ordering? - Local optimality is easy!
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Local optimality for model 1 min conversion

• Starting at first link, assign wavelength
  available for greatest number of consecutive
  links.
• Convert and continue on a different wavelength
  until the entire demand path is assigned
  wavelength(s).
• Strategy locally optimal

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Local optimality for model 1 min conversion

• Starting at first link, assign wavelength
  available for greatest number of consecutive
  links.
• Convert and continue on a different wavelength
  until the entire demand path is assigned
  wavelength(s).
• Strategy locally optimal

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Local optimality for model 2 Min fiber

• Choose wavelength w such that assigning w to
  demand d requires minimum number of extra fibers

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Local optimality for model 2 Min fiber

• Choose wavelength w such that assigning w to
  demand d requires minimum number of extra fibers

Extra fiber on first link
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Ordering in Greedy approach

• Global ordering
• Longest first Order demands according to number
  of links each demand travels.
• Heaviest Weigh each link according to the
  number of demands that traverse it. Sum the
  weights on each link of a demand.
• Ordering suggested by vertex coloring on demand
  graph
• Random sampling choose a random permutation.

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Ordering in Greedy approach

• Local perturbation d1, d2, d3, d4,
• Coin toss
• Reshuffle initial demand ordering by
• Flipping a coin for each entry in order
• With a success, remove the demand and move it to
  new ordering
• 2. Top-n
• Reshuffle initial demand ordering by
• Randomly choosing a first n demands
• Removing the demand to new ordering

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Iterative refinement
Global ordering
Greedy
Local perturbation
Greedy
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Generating instances

• Characteristics of network topology
• Sparse networks average node degree lt 3
• Planar
• Small networks ( 20 nodes) Large network ( 50
  nodes)
• Characteristics of traffic
• Fiber Capacity 20,100
• Lightly loaded networks 1 fiber per link, fibers
  half full
• Heavily loaded networks 2 fibers per links

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Topologies of real networks
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Topologies of real networks
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Topologies of real networks
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Experimental data
Group 1 real networks (light load)
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Experimental data
Group 1 real networks (light load)
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Probability of No Wavelength Conflict vs. Link
Load

• O(log u) approx.
• choose a wavelength
• uniformly at random
• for each demand
• Birthday Paradox!

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Experimental data
Group 2 simulated networks (heavy small)
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Experimental data
Group 2 simulated networks (heavy small)
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Experimental data Large Networks
Group 3 simulated networks (heavy large)
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Experimental data
Group 3 simulated networks (heavy large)
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Summary Preliminary observations

• Small light (real networks)
• All greedy solutions close to optimal
• Log approx behaves poorly
• Small heavy
• Random sampling has advantage
• Longest/heaviest less meaningful for shortest
  paths in small networks
• Large heavy
• Longest/heaviest more meaningful

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Combined minimization

• New territory
• Ultimate cost optimization
• Combined minimization of fiber and conversion
• Proposed approach
• Compute a min fiber solution (x extra fibers)
• From empty network, add one fiber at a time
• Compute a min conversion solution for fixed
  additional fibers.

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Combined minimization
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QUESTIONS???