How does split horizon help reduce the count-to-infinity problem in distance…

Concept

In distance-vector routing protocols (such as RIP), each router learns routes from its neighbors and re-advertises them onward. The count-to-infinity problem occurs when a route becomes unreachable but two neighboring routers keep advertising it to each other with steadily increasing hop counts, because each one still believes the other has a valid path. Split horizon is a loop-avoidance rule: a router omits a route from the update it sends out the very interface through which it originally learned that route, since re-advertising it there would just be echoing the neighbor’s own information back to it.

Application

Consider router B, which learns a route to network X from neighbor A on the link between them. Under split horizon, B does not include that route to X in the update it sends back to A on that same link. So if the link between A and X later fails, A does not receive a stale route to X from B claiming a working path via B, which is exactly the false information that would otherwise make A and B keep raising their advertised hop counts to each other toward infinity.

Cross-check

Contrast this with the other offered mechanisms. Suppressing updates on every port (rather than only the interface a specific route was learned on) would stop the router from advertising anything at all, which is not split horizon's selective, per-route, per-interface behaviour. Choosing distance over hop count is a metric-design decision (as in EIGRP), unrelated to which interface an update is withheld from. Turning off periodic updates concerns the update schedule (related instead to triggered updates), not the direction in which a specific route is withheld. RFC 1058 describes exactly this interface-specific withholding behaviour, confirming that preventing a router from advertising a route back on the interface it was learned from is the mechanism that reduces count-to-infinity here.