$1.$ Given a balanced binary tree describe a procedure to perform all$-$to$-$all broadcast that takes time $($ts $+$ tw$*$m$*$p$/2)$ log$2$ p for m$-$word messages on p nodes. Assume that only the leaves of the tree contain nodes, and that an exchange of two m$-$word messages between any two nodes connected by bidirectional channels takes time ts $+$ tw$*$m$*$k if the communication channel $($or a part of it$)$ is shared by k simultaneous messages.