Dijkstra's Algorithm: Shortest Path Finding in a Graph, Slides of Computer Networks

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Distance Vector Routing

How Distance-Vector (DV) works

Each router maintains its shortest distance to every

destination via each of its neighbors

via B via C to B to C to D

From node A

Neighbor

(next-hop)

Destinations dist

C (A, D): shortest

distance from A to D via C

A

How Distance-Vector (DV) works

How does A initialize its dist() table and DV?

via B via C to B?? to C?? to D??

From node A

A

min dist to B? to C? to D?

A’s DV

How Distance-Vector (DV) works

A

B

C

Link costs

How does A initialize its dist() table and DV?

How Distance-Vector (DV) works

Each router sends its DV to its immediate neighbors

via B via C

to B c (A,B) ∞

to C ∞ c (A,C) to D ∞ ∞

From node A

A

B

C

mindist to B c(A,B) to C c(A,C) to D ∞

A’s DV

mindist to B 5 to C 6 to D 2

How Distance-Vector (DV) works

Routers process received DVs

A

B

C

A’s DV

mi n to B 5 to C 6 to D 2 via A via C

to A 5 ∞

to C 15 1 to D ∞ ∞

From node B B’s DV

mindist to A 5 to C 1 to D ∞

Distance Vector Routing

• Each router knows the links to its neighbors
• Each router has provisional “shortest path” to every other router -- its distance vector (DV)
• Routers exchange this DV with their neighbors
• Routers look over the set of options offered by their neighbors and select the best one
• Iterative process converges to set of shortest paths

Distance Vector

• c(i,j): link cost from node i to j
• distZ(A,V): shortest dist. from A to V via Z
• mindist(A,V): shortest dist. from A to V 0 At node A 1 Initialization: 2 for all destinations V do 3 if V is neighbor of A 4 distV( A, V ) = mindist(A,V) = c( A,V ); 5 else 6 distV( A, V ) = mindist(A,V) = ∞; 7 send mindist( A, * ) to all neighbors loop: 8 wait (until A sees a link cost change to neighbor V /* case 1 / 9 or until A receives mindist(V,) from neighbor V ) /* case 2 / 10 if (c( A , V ) changes by ± d ) /  case 1 / 11 for all destinations Y do 12 distV( A,Y ) = distV( A,Y ) ± d 13 else /  case 2: / 14 for all destinations Y do 15 distV( A,Y ) = c( A,V ) + mindist( V, Y ); 16 update mindist( _A,_ ) 15 if (there is a change in mindist(A, *)) 16 send mindist( A, * ) to all neighbors 17 forever

Example: Initialization via B via C to A - - to B 2 ∞ to C ∞ 7 to D ∞ ∞

A C

B D

from Node A via A via C via D to A 2 ∞ ∞ to B - - - to C ∞ 1 ∞ to D ∞ ∞ 3 from Node B from Node C via A via B via D to A 7 ∞ ∞ to B ∞ 1 ∞ to C - - - to D ∞ ∞ 1 via B via C to A ∞ ∞ to B 3 ∞ to C ∞ 1 to D - - from Node D min dist to A 0 to B 2 to C 7 to D ∞ min dist 0 2 7 ∞ min dist 2 0 1 3 min dist ∞ 3 1 0 min dist 7 1 0 1

Example: C sends update to A via B via C to A - - to B 2 ∞ to C ∞ 7 to D ∞ ∞ from Node A via A via C via D to A 2 ∞ ∞ to B - - - to C ∞ 1 ∞ to D ∞ ∞ 3 from Node B from Node C via A via B via D to A 7 ∞ ∞ to B ∞ 1 ∞ to C - - - to D ∞ ∞ 1 via B via C to A ∞ ∞ to B 3 ∞ to C ∞ 1 to D - - from Node D min dist 0 2 7 ∞ min dist ∞ 3 1 0 min dist 7 1 0 1

A C

B D

min dist 2 0 1 3

Example: C sends update to A via B via C to A - - to B 2 8 to C ∞ 7 to D ∞ 8 from Node A min dist 0 2 7 ∞

A C

B D

min dist 7 1 0 1

Example: C sends update to A via B via C to A - - to B 2 8 to C ∞ 7 to D ∞ 8 from Node A min dist 0 2 7 8

A C

B D

Example: now B sends update to A via A via C via D to A 2 ∞ ∞ to B - - - to C ∞ 1 ∞ to D ∞ ∞ 3 from Node B from Node C via A via B via D to A 7 ∞ ∞ to B ∞ 1 ∞ to C - - - to D ∞ ∞ 1 via B via C to A ∞ ∞ to B 3 ∞ to C ∞ 1 to D - - from Node D min dist ∞ 3 1 0 min dist 7 1 0 1

A C

B D

min dist 2 0 1 3 via B via C to A - - to B 2 8 to C ∞ 7 to D ∞ 8 from Node A min dist 0 2 7 (^8) docsity.com

Example: now B sends update to A via A via C via D to A 2 ∞ ∞ to B - - - to C ∞ 1 ∞ to D ∞ ∞ 3 from Node B from Node C via A via B via D to A 7 ∞ ∞ to B ∞ 1 ∞ to C - - - to D ∞ ∞ 1 via B via C to A ∞ ∞ to B 3 ∞ to C ∞ 1 to D - - from Node D min dist ∞ 3 1 0 min dist 7 1 0 1

A C

B D

min dist 2 0 1 3 via B via C to A - - to B 2 8 to C 3 7 to D 5 8 from Node A min dist 0 2 7 8 Make sure you know why this is 5, not 4!