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#
Authors:
James F. Kurose, Keith W. Ross
Chapter:
The Network Layer
Exercise:
Problems
Question:27 | ISBN:9780132856201 | Edition: 6

Question

Consider the network shown in Problem P26. Using Dijkstra’s algorithm, and showing your work using a table similar to Table 4.3, do the following:

a. Compute the shortest path from t to all network nodes.

b. Compute the shortest path from u to all network nodes.

c. Compute the shortest path from v to all network nodes.

d. Compute the shortest path from w to all network nodes.

e. Compute the shortest path from y to all network nodes.

f. Compute the shortest path from z to all network nodes.

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Answer

Refer the Dijkstra’s algorithm and the problem 26 in the text book.

a)

The shortest path from t to all network nodes:

Num

N’

D(u),p(u)

D(v),p(v)

D(w),p(w)

D(x),p(x)

D(y),p(y)

D(z),p(z)

0

t

2,t

4,t

\infty

\infty

7,t

\infty

1

tu

2,t

4,t

5,u

\infty

7,t

\infty

2

tuv

2,t

4,t

5,u

7,v

7,t

\infty

3

tuvw

2,t

4,t

5,u

7,v

7,t

\infty

4

tuvwx

2,t

4,t

5,u

7,v

7,t

15,x

5

tuvwxy

2,t

4,t

5,u

7,v

7,t

15,x

6

tuvwxyz

2,t

4,t

5,u

7,v

7,t

15,x

   Here, assume N'=subset of nodes, D(v)= The path from the source to the destination for the node,v. p(v)=The path with least cost from source to node, v. 

b)

The shortest path from u to all network nodes:

Num

N’

D(t),p(t)

D(v),p(v)

D(w),p(w)

D(x),p(x)

D(y),p(y)

D(z),p(z)

0

u

2,u

3,u

3,u

\infty

\infty

\infty

1

ut

2,u

3,u

3,u

\infty

9,t

\infty

2

utv

2,u

3,u

3,u

6,v

9,t

\infty

3

utvw

2,u

3,u

3,u

6,v

9,t

\infty

4

utvwx

2,u

3,u

3,u

6,v

9,t

14,x

5

utvwxy

2,u

3,u

3,u

6,v

9,t

14,x

6

utvwxyz

2,u

3,u

3,u

6,v

9,t

14,x

c)

The shortest path from v to all network nodes:

Num

N’

D(t),p(t)

D(u),p(u)

D(w),p(w)

D(x),p(x)

D(y),p(y)

D(z),p(z)

0

v

4,v

3,v

4,v

3,v

8,v

\infty

1

vx

4,v

3,v

4,v

3,v

8,v

11,x

2

vxu

4,v

3,v

4,v

3,v

8,v

11,x

3

vxut

4,v

3,v

4,v

3,v

8,v

11,x

4

vxutw

4,v

3,v

4,v

3,v

8,v

11,x

5

vxutwy

4,v

3,v

4,v

3,v

8,v

11,x

6

vxutwyz

4,v

3,v

4,v

3,v

8,v

11,x

d)

The shortest path from w to all network nodes:

Step

N’

D(t),p(t)

D(u),p(u)

D(v),p(v)

D(x),p(x)

D(y),p(y)

D(z),p(z)

0

w

 

3,w

4,w

6,w

\infty

\infty

1

wu

5,u

3,w

4,w

6,w

\infty

\infty

2

wuv

5,u

3,w

4,w

6,w

12,v

\infty

3

wuvt

5,u

3,w

4,w

6,w

12,v

\infty

4

wuvtx

5,u

3,w

4,w

6,w

12,v

14,x

5

wuvtxy

5,u

3,w

4,w

6,w

12,v

14,x

6

wuvtxyz

5,u

3,w

4,w

6,w

12,v

14,x
0 0

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