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Distance-vector Algorithms

CSE 313: Computer Networks

SR Kohinoormdsaidur.r.kohinoor@ieee.org

G

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Distance vector: Each node sends list of its shortest distance to reach

each of its directly connected neighbors.

Algorithm:

o Bellman-Ford algorithm

Distributed route computation using only neighbors

information.

o Iterative, asynchronous: eachlocal iteration caused by:

Local link cost change Distance vector update message from neighbor

o Distributed:Each node notifies neighbors only when its DV changes

Neighbors then notify their neighbors if necessary.

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Bellman-Ford Algorithm:

Define distances at each node X dx(y) = cost of least-cost pathfrom Xto Y

Update distances based on neighbors

dx(y) = min {c(x,v) + dv(y)} over all neighbors V

3

V 2 y

1 x 4U

2 1

5

w 4 3

s

1

z

t

du(z) = min{c(u,v) + dv(z), c(u,w) + dw(z)}

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Step-by-Step:

c(x,v)=cost for direct link fromxtov Node x maintains costs of direct links c(x,v)

Dx(y)=estimate of least cost fromxtoy

Node xmaintains distance vector Dx= [Dx(y): yN ]

Node xmaintains its neighborsdistance vectors

For each neighbor v, xmaintains Dv= [Dv(y): yN ]

Each node vperiodically sends Dvto its neighbors

And neighbors update their own distance vectors

Dx(y) minv{c(x,v) + Dv(y)}for each nodeyN

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Example: Initial State

7

B 1 C

A 8 2

1

E 2 D

Info atDistance to Node

A B C D Enode

A 0 7 1

B 7 0 1 8

C 1 0 2

D 2 0 2

E 1 8 2 0

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D sends vector toE

Im 2 from C, 0 from

D and 2 from E

7

B 1 C

A 8 2

1

E2

D

D is 2 away, 2+2< ,

so best path to C is 4

Info atDistance to Node

A B C D Enode

A 0 7 1

B 7 0 1 8

C 1 0 2

D 2 0 2

E 1 8 4 2 0

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B sends vector toA

7

A

1

Im 7 from A, 0

from B, 1 from C

& 8 from E

B 1 C

8 2

E 2 D

B is 7 away, 1+7< so

best path to C is 8

Info atDistance to Node

A B C D Enode

A 0 7 8 1

B 7 0 1 8

C 1 0 2

D 2 0 2

E 1 8 4 2 0

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E sends vector toA

E is 1 away, 4+1

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until Convergence

7

B 1 C

A 8 2

1

E2

D

Info atDistance to Node

A B C D Enode

A 0 6 5 3 1

B 6 0 1 3 5

C

5

1

0

2

4

D 3 3 2 0 2

E 1 5 4 2 0

22

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Node Bs distance vectors

7

B 1 C

A 8 2

1

E2

D

Next hop

Dest A E C

A 7 9 6

C 12 12 1

D 10 10 3

E 8 8 5

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Handling Link Failure

A marks distance to E as , and tells B

E marks distance to A as , and tells B and D

B and D recompute routes and tell C, E and E etc until converge

Info Distance to Node

B 1 C at

A B C D E7 node

A 8 2A 0 7 8 10 12

B 7 0 1 3 5

E 2 D C

8

1

0 2 4

D 10 3 2 0 2

E 12 5 4 2 0

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THANK YOU