Information theoretic approaches are increasingly being used for reconstructing regulatory networks from microarray data. These approaches start by computing the pairwise mutual information (MI) between all gene pairs. The resulting MI matrix is then manipulated to identify regulatory relationships. A barrier to these approaches is the time-consuming step of computing the MI matrix. We present a method to reduce this computation time. We apply spectral analysis to re-order the genes, so that genes that share regulatory relationships are more likely to be placed close to each other. Then, using a "sliding window" approach with appropriate window size and step size, we compute the MI for the genes within the sliding window, and the remainder is assumed to be zero. Using both simulated data and microarray data, we demonstrate that our method does not incur performance loss in regions of high-precision and low-recall, while the computational time is significantly lowered. The proposed method can be used with any method that relies on the mutual information to reconstruct networks.