$4\mathrm{.}0.($This exercise assumes some familiarity with Distance$-$Vector routing as in

Algorithms.$)$

$($a$).$ Suppose switches are able to identify the non$-$switch hosts that are directly connected, that is$,$

reachable without passing through another switch. Explain how the algorithm of $13\mathrm{.}1$ Distance$-$

Vector Routing$-$Update Algorithm could be used to construct optimal Ethernet forwarding tables

even if loops were present in the network topology.

$($b$).$ Suppose switches are allowed to "mark" packets; all packets are initially unmarked. Give a

mechanism that allows switches to detect which non$-$switch hosts are directly connected.

$($c$).$ Explain why Ethernet broadcast $($and multicast$)$ would still be a problem.