  The PC algorithm is the state-of-the-art algorithm for causal structure
discovery on observational data. It can be computationally expensive in the
worst case due to the conditional independence tests are performed in an
exhaustive-searching manner. This makes the algorithm computationally
intractable when the task contains several hundred or thousand nodes,
particularly when the true underlying causal graph is dense. We propose a
critical observation that the conditional set rendering two nodes independent
is non-unique, and including certain redundant nodes do not sacrifice result
accuracy. Based on this finding, the innovations of our work are two-folds.
First, we innovate on a reserve order linkage pruning PC algorithm which
significantly increases the algorithm's efficiency. Second, we propose a
parallel computing strategy for statistical independence tests by leveraging
tensor computation, which brings further speedup. We also prove the proposed
algorithm does not induce statistical power loss under mild graph and data
dimensionality assumptions. Experimental results show that the single-threaded
version of the proposed algorithm can achieve a 6-fold speedup compared to the
PC algorithm on a dense 95-node graph, and the parallel version can make a
825-fold speed-up. We also provide proof that the proposed algorithm is
consistent under the same set of conditions with conventional PC algorithm.
