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Homework 6 Local Access Design

• Given the topology below, the weight of each node
  is 1, and W 3
• a) apply the greedy CMST algorithm.
• b) apply the Esau-Williams algorithm.
• Highlight the trees (components) selected.

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Solution to Hw6

• Solution a) Greedy MST. First sort the edge cost
  in increasing order.

Edge Cost CMST Decision
(1,4) 1 select
(2,3) 1 select
(0,1) 2 select
(3,5) 2 select
(0,5) 5 Select, Done!
(2,4) 5
(1,2) 6
(1,3) 7
(0,2) 8
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Solution to Hw6(2)

• Solution b) Esau-Williams Algorithm
• begin by computing the tradeoffs for the nearest
  neighbors of each node (since that link will have
  smallest cost and yield a low trade-off
  values) t14 c14 - cc1 1 - 2 -1 t23
  1 - 8 -7 t32 1 - 11 -10 t41 1 - 14
  -13 t53 c53 - cc5 2 - 5 -3
• starting with t41 which is the lowest tradeoff
  value, we add link (4,1) to subtrees,now cc4 2
  since node 4 now connected to the center through
  node 1, find the next nearest neighbor of 1 to
  be 0, t102-20let us now compute the tradeoff
  between node 4 and the next nearest neighbor to
  node 4 (which is node 2), t42 c42 - cc4 5
  -2 3

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Solution to Hw6(3)

• Now t32 has the lowest tradeoff value, add link
  (3,2) to the subtrees,now cc3 8 and the next
  nearest neighbor to node 3 is 5, t35 2 - 8
  -6
• We also need to update t23 since (2,3) is chosen.
  
• The next nearest neighbor to node 2 is 4,
• t24 5 - 8 -3
• Select t35-6, add link(3,5) to the subtrees. N
• ow Cc2Cc3Cc55, we need to update
• t317-52
• t245-50
• t505-50
• Select (1,0) add link (1,0) to the subtrees.
• Reject (2,4) since it will create a component of
  weight 4.
• Select (5,0) add link (5,0) to the subtrees.
• Now all nodes are connected to node 0.
• Note that the algorithm always terminates with
  links whose tradeoffs are 0. We will never
  consider any links with positive tradeoff.

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Solution to Hw6(4)

• The solution has a cost of 11.
• Both EW algorithm and GMST find optimal solution
  but GMST is much faster.