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Telcom 2110 Network Design
Homework #3 Solution, Spring
2010
1.
Consider the network below with the link cost shown adjacent to the link. Determine a MST
using Prim’s algorithm starting at node D
Step 1.
6
2
Step 2.
Step 3.
Step 4.
Step 5.
Step 6.
The MST cost is 17.
B
A
D
C
E
F
5
2
4
6
10
4
6
2
9
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Repeat problem 1
using Dijkstra’s algorithm to construct a shortest path tree starting at D
for your SPT network.
Compare the results with the MST result from problem 1.
Iteration
T
Path
d_min(B)
Path
d_min(C)
Path
d_min(E)
Path
d_min(F)
Path
1
{D}
6
(D,A)
4
(D,B)
10
(D,C)

6
(D,F)
2
{D,B}
6
(D,A)
4
(D,B)
10
(D,C)

6
(D,F)
3
{D,B,F}
6
(D,A)
4
(D,B)
8
(D,F)(F,C)
15
(D,F)(F,E)
6
(D,F)
4
{D,B,F,A}
6
(D,A)
4
(D,B)
8
(D,F)(F,C)
15
(D,F)(F,E)
6
(D,F)
5
{D,B,F,A,C}
6
(D,A)
4
(D,B)
8
(D,F)(F,C)
12
(D,F)(F,C)(C,E)
6
(D,F)
6
{D,B,F,A,C,E}
6
(D,A)
4
(D,B)
8
(D,F)(F,C)
12
(D,F)(F,C)(C,E)
6
(D,F)
The SPT cost is 22.
When comparing the two solutions, it is noted that network cost for connecting between
D and any network node is improved using Dijkstra’s algorithm. However, the overall network
cost significantly increases with this method.
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 Spring '10
 D>Tipper

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