CS622 Page 1

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Homework 5

• Problem 1. Network Restoration.
• For link A-G cut, show the restoration paths
  (route as sequence of nodes, and itsrestored
  bandwidth.
• Discuss the selection trade-offfor the two
  algorithms at Page5 handout.
• Problem 2. Tree and Tour.
• Problem 3.7.
• Explain why for the 20-node random problem
  avg(hops)SPT1.9000.
• Prove for a start on n nodes,S, that
  avg(hops)S2-2/n.
• Download the g20sw. from cs622/public_html/delit
  e.Run delite with 1. Tour (Nearest Neighbor), 2.
  Tour (Furthest Neighbor), 3. Prim, 4. SPT.
  Compare the cost, avg(hops), and max. utilization
  of these four designs.

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Solution to HW5

• Problem 1. Network Restoration
• For link A-G cut, show the restoration paths
  (route as sequence of nodes, and its restored
  bandwidth.
• Ans 8 working channels lost.3 restoration paths
  through AFG.2 restoration paths through ACEFG
• b. Discuss the selection trade-offfor the two
  algorithms at Page5 handout.
• Ans Depends on the restoration deadline and
  whether restoration paths are needed earlier for
  the priority traffic.If the restoration level is
  the utmost important metric, then the final
  restorationlevel at the restoration deadline
  decides theselection of the algorithm. The
  curve however does not show the spare channel
  usage.

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Solution to HW5 (2)

• Problem 2. Tree and Tour.
• Problem 3.7.
• Explain why for the 20-node random problem
  avg(hops)SPT1.9000.
• Prove for a star on n nodes,S, that
  avg(hops)S2-2/n.
• Ans 1 There are c(20,2)2019/2190
  connections.Among them, 19 are to the
  star.avg(hops)spt((190-19)2191)/1901.9
• Ans 2 There are c(n,2)n(n-1)/2
  connections.Among them, n-1 are to the
  star.Avg(hops)S(n(n-1)/2-(n-1))2(n-1))/(n(n-
  1)/2)(n(n-1)-(n-1))/(n(n-1)/2)2(n-1)/n2-2/n
  .
• Download the g20sw. from cs622/public_html/delit
  e.Run delite with 1. Tour (Nearest Neighbor), 2.
  Tour (Furthest Neighbor), 3. Prim, 4. SPT.
  Compare the cost, avg(hops), and max. utilization
  of these four designs.

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Delite Tool Analysis (Tour NN)
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Tour (Furthest Neighbor)
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PRIM
7
SPT
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Network Design Comparison
NetworkDesign Cost Avg HopCount Max Utilization
TourNearestNeigbbor 62732 5.2632 0.005
TourFurtherNeighbor 55061 5.2623 0.005
Prim(MST) 48610 5.0316 0.010
SPT 103650 1.9 0.002