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Given a set V of n sensor node distributed on a 2-dimensional plane and a source node s ∈ V, the interference problem deals with assigning transmission range to each v ∈ V such that the members in V maintain connectivity predicate P, and the maximum/total interference is minimum. We propose algorithm for both minimizing maximum interference and minimizing total interference of the networks. For minimizing maximum interference we present optimum solution with running time O((Pn + n 2 ) log n) for connectivity predicate P like strong connectivity, broadcast (s is the source), k-edge(vertex) connectivity, spanner, where O(Pn) is the time complexity for checking the connectivity predicate P. The running time of the previous best known solution was O(Pn × n 2 ) [3]. 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 [3]. 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.