  It is shown that in the K-user interference channel, if for each user the
desired signal strength is no less than the sum of the strengths of the
strongest interference from this user and the strongest interference to this
user (all values in dB scale), then the simple scheme of using point to point
Gaussian codebooks with appropriate power levels at each transmitter and
treating interference as noise at every receiver (in short, TIN scheme)
achieves all points in the capacity region to within a constant gap. The
generalized degrees of freedom (GDoF) region under this condition is a
polyhedron, which is shown to be fully achieved by the same scheme, without the
need for time-sharing. The results are proved by first deriving a polyhedral
relaxation of the GDoF region achieved by TIN, then providing a dual
characterization of this polyhedral region via the use of potential functions,
and finally proving the optimality of this region in the desired regime.
