Consider the following three statements about link state and distance vector…

Answer: S1 and S3 are true; S2 is false.

• Statement S1: The computational overhead in link-state protocols is higher than in distance-vector protocols.

  Explanation: True. Each link-state router builds and stores the full network topology and runs a shortest-path algorithm (e.g., Dijkstra). That increases CPU and memory requirements per router compared with distance-vector protocols, which keep only next-hop distance information and update iteratively. In a large network (500 nodes, 4000 links) this per-router computation and memory usage become significant.

• Statement S2: A distance vector protocol (with split horizon) avoids persistent routing loops, but not a link-state protocol.

  Explanation: False. Split horizon and related techniques reduce simple loop scenarios but do not eliminate problems like count-to-infinity or persistent incorrect routes in distance-vector protocols. Link-state protocols, by contrast, distribute consistent topology information and each router computes complete shortest-path trees; given consistent link-state databases, they do not produce persistent routing loops (though transient loops can occur during convergence).

• Statement S3: After a topology change, a link-state protocol will converge faster than a distance-vector protocol.

  Explanation: True. Link-state routers flood link-state advertisements to quickly inform all routers of the change, and each router recomputes routes locally. Distance-vector protocols rely on iterative neighbor-to-neighbor updates that can take many iterations to propagate and stabilize, especially in large topologies, so convergence is typically slower.

Conclusion: S1 and S3 are correct; S2 is incorrect. Therefore the correct choice is the one stating that S1 and S3 are true and S2 is false.