  A fundamental problem in wireless sensor networks is to connect a given set
of sensors while minimizing the \emph{receiver interference}. This is modeled
as follows: each sensor node corresponds to a point in $\mathbb{R}^d$ and each
\emph{transmission range} corresponds to a ball. The receiver interference of a
sensor node is defined as the number of transmission ranges it lies in. Our
goal is to choose transmission radii that minimize the maximum interference
while maintaining a strongly connected asymmetric communication graph.
  For the two-dimensional case, we show that it is NP-complete to decide
whether one can achieve a receiver interference of at most $5$. In the
one-dimensional case, we prove that there are optimal solutions with nontrivial
structural properties. These properties can be exploited to obtain an exact
algorithm that runs in quasi-polynomial time. This generalizes a result by Tan
et al. to the asymmetric case.
