Let $P$ be a set of $n$ points on the $x-$axis, let $s$ be an additional point on the $x-$axis representing

the source transmitter.

In the broadcast in $2$ hops problem we are required to determine the transmission ranges of

the transmitters in $P\{s\}$ such that:

a$.$ In the directed communication graph, there is a path of length at most $2$ from $s$ to each $p$

in $P.$

b$.$ The sum of ${\displaystyle \underset{\text{p}\text{i}\text{n}\text{P}\{s\}}{\overset{?}{}}}r(p{)}^{}$ is minimal where $r(p)0$ is the range set for $p.$

Propose an algorithm for the case $=1$

Propose an algorithm for the case $=2.$