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Reconstructing the topology of a signaling network by means of RNA interference (RNAi) technology is an underdetermined problem especially when a single gene in the network is knocked down or observed. In addition, the exponential search space limits the existing methods to small signaling networks of size 10-15 genes. In this paper, we propose integrating RNAi data with a reference physical interaction network. We formulate the problem of signaling network reconstruction as finding the minimum number of edit operations on a given reference network. The edit operations transform the reference network to a network that satisfies the RNAi observations. We show that using a reference network does not simplify the computational complexity of the problem. Therefore, we propose two methods which provide near optimal results and can scale well for reconstructing networks up to hundreds of components. We validate the proposed methods on synthetic and real data sets. Comparison with the state of the art on real signaling networks shows that the proposed methodology can scale better and generates biologically significant results.