Before revision:  The cuPC algorithm has two variants, cuPC-E and cuPC-S, which parallelize conditional independence tests over the pairs of variables under the tests, and over the conditional sets, respectively. In particular, cuPC-E offers two degrees of parallelization by performing tests of multiple pairs of variables and also the tests of each pair in parallel. In the other hand, cuPC-S reuses the results of computations of a test for a given conditional set in other tests on the same conditional set. Experiment results on GTX 1080 GPU show two to three orders of magnitude speedup.
After revision:  The cuPC algorithm has two variants, cuPC-E and cuPC-S, which parallelize PC in two different ways. Experimental results show significant speedup.