  A network where three users want to establish multiple unicasts between each
other via a relay is considered. This network is called the Y-channel and
resembles an elemental ingredient of future wireless networks. The sum-capacity
of this network is studied. A characterization of the sum-capacity within an
additive gap of 2 bits, and a multiplicative gap of 4, for all values of
channel gains and transmit powers is obtained. Contrary to similar setups where
the cut-set bounds can be achieved within a constant gap, they can not be
achieved in our case, where they are dominated by our new genie-aided bounds.
Furthermore, it is shown that a time-sharing strategy, in which at each time
two users exchange information using coding strategies of the bi-directional
relay channel, achieves the upper bounds to within a constant gap. This result
is further extended to the K-user case, where it is shown that the same scheme
achieves the sum-capacity within 2log(K-1) bits.
