Dynamic biological systems, such as gene regulatory networks (GRNs) and protein signaling networks, are often represented as systems of ordinary differential equations. Such equations can be utilized in reverse engineering these biological networks, specifically since identifying these networks is challenging due to the cost of the necessary experiments growing with at least the square of the size of the system. Moreover, the number of possible models, proportional to the number of directed graphs connecting nodes representing the variables in the system, suffers from combinatorial explosion as the size of the system grows. Therefore, exhaustive searches for systems of nontrivial complexity are not feasible. Here we describe a practical and scalable algorithm for determining candidate network interactions based on decomposing an N-dimensional system into N one-dimensional problems. The algorithm was tested on in siliconetworks based on known biological GRNs. The computational complexity of the network identification is shown to increase as N2 while a parallel implementation achieves essentially linear speedup with the increasing number of processing cores. For each in silico network tested, the algorithm successfully predicts a candidate network that reproduces the network dynamics. This approach dramatically reduces the computational demand required for reverse engineering GRNs and produces a wealth of exploitable information in the process. Moreover, the candidate network topologies returned by the algorithm can be used to design future experiments aimed at gathering informative data capable of further resolving the true network topology.