Two popular routing algorithms are Distance Vector(DV) and Link State (LS)…

Final answer: S1 and S4 only.

• S1 — True: Count-to-infinity is a known convergence problem in Distance Vector routing because routers exchange only distance vectors and can iteratively increase metrics without global topology knowledge. Link State routers have a complete topology and use Dijkstra, so they do not exhibit the classic count-to-infinity behavior.

• S2 — False: In Link State routing every router builds the full link-state database and runs the shortest-path algorithm (e.g., Dijkstra) locally. It is not run only at a single node.

• S3 — False: Distance Vector routing operates in a distributed manner; each node updates its routing information based on neighbors (Bellman-Ford style updates). There is no single node that alone runs the shortest-path algorithm for the entire network.

• S4 — True (textbook assertion): Distance Vector typically requires fewer network-wide messages because updates are exchanged between neighbors, whereas Link State floods link-state advertisements to all routers. Note: actual message overhead depends on network size and dynamics, but the standard comparison in many texts states DV has lower message count than LS.

Summary: S1 and S4 are true; S2 and S3 are false. The correct choice is the set containing S1 and S4 only.