  This paper considers a diamond network with $n$ interconnected relays, namely
a network where a source communicates with a destination by hopping information
through $n$ communicating/interconnected relays. Specifically, the main focus
of the paper is on characterizing sufficient conditions under which the $n+1$
states (out of the $2^{n}$ possible ones) in which at most one relay is
transmitting suffice to characterize the approximate capacity, that is the
Shannon capacity up to an additive gap that only depends on $n$. Furthermore,
under these sufficient conditions, closed form expressions for the approximate
capacity and scheduling (that is, the fraction of time each relay should
receive and transmit) are provided. A similar result is presented for the dual
case, where in each state at most one relay is in receive mode.
