The computational cost required to calculate nuclear correlation functions grows factorially in the number of quarks, making the study of large nuclei inaccessible to ab initio study using lattice QCD at the present time. However, the tensor expressions corresponding to many of these correlation functions exhibit a high degree of permutation symmetry that can be exploited to reduce computational work. We present promising speed-ups for certain choices of interpolating operators using two new algorithms for computing nuclear correlation functions.