In distance-vector routing, each router tells its neighbors its current best-known distance to destinations. A router combines a neighbor's advertised distance with the cost of reaching that neighbor and keeps the best alternative.

This is the distributed idea behind Bellman-Ford relaxation. If router A reaches B with cost 2 and B advertises destination D at cost 5, A obtains a candidate route to D with cost $2+5=7$.

The approach is local: A need not know the complete topology. But local information can propagate slowly after failures. Routers may temporarily reinforce one another's stale routes, producing loops or count-to-infinity behavior.

Techniques such as split horizon and route poisoning reduce particular failure modes, but the deeper lesson is that distributed shortest-path computation has convergence behavior that does not appear in an offline graph algorithm.