  Given a set ${\cal V}$ of $n$ sensor node distributed on a 2-dimensional
plane and a source node $s \in {\cal V}$, the {\it interference problem} deals
with assigning transmission range to each $v \in {\cal V}$ such that the
members in ${\cal V}$ maintain connectivity predicate ${\cal P}$, and the
maximum/total interference is minimum. We propose algorithm for both {\it
minimizing maximum interference} and {\it minimizing total interference} of the
networks. For minimizing maximum interference we present optimum solution with
running time $O(({\cal P}_n + n^2) \log n)$ for connectivity predicate ${\cal
P}$ like strong connectivity, broadcast ($s$ is the source), $k$-edge(vertex)
connectivity, spanner, where $O({\cal P}_n)$ is the time complexity for
checking the connectivity predicate ${\cal P}$. The running time of the
previous best known solution was $O({\cal P}_n \times n^2)$ [Bil$\grave{o}$ and
Proietti, 2008].
  For the minimizing total interference we propose optimum algorithm for the
connectivity predicate broadcast. The running time of the propose algorithm is
O(n). For the same problem, the previous best known result was $2(1 + \ln
(n-1))$-factor approximation algorithm [Bil$\grave{o}$ and Proietti, 2008]. We
also propose a heuristic for minimizing total interference in the case of
strongly connected predicate and compare our result with the best result
available in the literature. Experimental results demonstrate that our
heuristic outperform existing result.
