Consider a computer network using the distance vector routing algorithm in its network layer. The partial topology of the network is as shown below. The objective is to find the shortest-cost path from the router $R$ to routers $P$ and $Q$. Assume that $R$ does not initially know the shortest routes to $P$ and $Q$. Assume that $R$ has three neighbouring routers denoted as $X$, $Y$, and $Z$. During one iteration, $R$ measures its distance to its neighbours $X$, $Y$, and $Z$ as $3$, $2$, and $5$, respectively. Router $R$ gets routing vectors from its neighbours that indicate that the distance to router $P$ from routers $X$, $Y$, and $Z$ are $7$, $6$, and $5$, respectively. The routing vector also indicates that the distance to router $Q$ from routers $X$, $Y$, and $Z$ are $4$, $6$, and $8$, respectively. Which of the following statement(s) is/are correct with respect to the new routing table of $R$, after updation during this iteration?

In Distance Vector Routing, router $R$ updates its distance vector to any destination $D$ using the Bellman-Ford equation:

Given link costs from $R$ to its neighbors:

• $c(R, X) = 3$

• $c(R, Y) = 2$

• $c(R, Z) = 5$

1. For Destination $P$:

• Via neighbor $X$: $c(R, X) + d_X(P) = 3 + 7 = 10$

• Via neighbor $Y$: $c(R, Y) + d_Y(P) = 2 + 6 = 8$

• Via neighbor $Z$: $c(R, Z) + d_Z(P) = 5 + 5 = 10$

The minimum cost to reach $P$ is $\min(10, 8, 10) = 8$, and the corresponding next hop is $Y$.

• Statement (A) is incorrect (cost is $8$, not $10$).

• Statement (C) is correct (next hop is $Y$).

2. For Destination $Q$:

• Via neighbor $X$: $c(R, X) + d_X(Q) = 3 + 4 = 7$

• Via neighbor $Y$: $c(R, Y) + d_Y(Q) = 2 + 6 = 8$

• Via neighbor $Z$: $c(R, Z) + d_Z(Q) = 5 + 8 = 13$

The minimum cost to reach $Q$ is $\min(7, 8, 13) = 7$, and the corresponding next hop is $X$.

• Statement (B) is correct (stored distance is $7$).

• Statement (D) is incorrect (next hop is $X$, not $Z$).

Thus, statements (B) and (C) are correct.