 Solution

In reverse path forwarding, a router uses its unicast routing information to ask which interface it would use to send a packet back towards source $S$. It accepts a multicast packet from $S$ only when it arrives on that interface, and otherwise discards it. An accepted packet can be forwarded on the other eligible interfaces. This needs no globally computed multicast distribution tree before the first transmission.^[ref]

With stable, loop-free routes and a consistent choice of parent when routes tie, each non-source router selects one upstream parent towards $S$. Following parent links reaches $S$, so the accepted parent links form a source-rooted tree over reachable routers. A packet arriving across a cross-link from a non-parent fails the reverse-path test. Basic flooding can still transmit copies that will be discarded; downstream-neighbour information can suppress such useless transmissions, and a designated forwarder prevents duplicate delivery on a shared local network.

To adapt the forwarding structure to a particular multicast group, retain branches with local members or interested descendants and prune the others. Leaf routers with no interested receivers initiate pruning; a router with no local members and no remaining interested children can propagate that condition upstream. A new subscriber requires a join/graft or later refresh to restore a pruned branch. Thus reverse path forwarding gives the source-rooted reachability structure, while membership and pruning restrict it to useful branches.

This tree need not minimize total transmission cost. Even if the unicast routes are shortest paths under symmetric positive link costs, their union minimizes individual distances from the source, rather than the sum of the costs of all used links. For a small example, let $SA$ and $SB$ each cost 2 and let $AB$ cost 1, with receivers at $A$ and $B$. The shortest-path tree uses $SA$ and $SB$, costing 4 in total. Using $SA$ and $AB$ costs 3, although the route from $S$ to $B$ then has length 3 instead of 2. Moreover, real unicast policies may optimize other criteria, and reverse routes need not be best forward routes when costs are asymmetric. Therefore