Consider a network with five nodes, N1 to N5, as shown below. The network uses a Distance Vector Routing protocol. Once the routes have stabilized, the distance vectors at different nodes are as following. N1: (0, 1, 7, 8, 4) N2: (1, 0, 6, 7, 3) N3: (7, 6, 0, 2, 6) N4: (8, 7, 2, 0, 4) N5: (4, 3, 6, 4, 0) Each distance vector is the distance of the best known path at that instance to nodes, N1 to N5, where the distance to itself is 0. Also, all links are symmetric and the cost is identical in both directions. In each round, all nodes exchange their distance vectors with their respective neighbors. Then all nodes update their distance vectors. In between two rounds, any change in cost of a link will cause the two incident nodes to change only that entry in their distance vectors. The cost of link N2-N3 reduces to 2 (in both directions). After the next round of updates, what will be the new distance vector at node, N3?

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Solution

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Official answer: A) (3, 2, 0, 2, 5)

Distance Vector and Link-State Routing

Before the update, the distance vectors received by node $N_3$ from its direct neighbors ( $N_2$ and $N_4$ ) are:

From $N_2$ : $(1, 0, 6, 7, 3)$
From $N_4$ : $(8, 7, 2, 0, 4)$

The new link costs incident to $N_3$ are:

$c(N_3, N_2) = 2$
$c(N_3, N_4) = 2$

Node $N_3$ updates its distance vector using the Bellman-Ford equation:

D_{N_3}(X) = \min \{ c(N_3, N_2) + D_{N_2}(X), \; c(N_3, N_4) + D_{N_4}(X) \}

Let us compute the distance from $N_3$ to each destination node:

To $N_1$ : $\min(2 + 1, 2 + 8) = \min(3, 10) = 3$
To $N_2$ : $\min(2 + 0, 2 + 7) = \min(2, 9) = 2$
To $N_3$ : $0$
To $N_4$ : $\min(2 + 7, 2 + 0) = \min(9, 2) = 2$
To $N_5$ : $\min(2 + 3, 2 + 4) = \min(5, 6) = 5$

Thus, the updated distance vector at node $N_3$ is $(3, 2, 0, 2, 5)$ .

Therefore, option A is the correct choice.

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This Distance Vector and Link-State Routing previous year question is Q52 of the GATE CSE 2011 paper. Find more GATE CSE PYQs on Distance Vector and Link-State Routing in Computer Networks, or browse all GATE CSE PYQs.

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Distance Vector and Link-State Routing in GATE CSE

Distance Vector and Link-State Routing has 9 GATE CSE PYQs across 8 papers from 2011 to 2025. 2 of them are 2-mark MCQs like this one, and GATE CSE 2011 has 2.

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