Before revision:  In fact, the decomposition-based algorithm usually outperforms the PC-like algorithm . We empirically show that the results of both algorithms are more accurate and stable when the sample size is reasonably large and the underlying graph is sparse.
After revision:  In fact, the decomposition-based algorithm usually outperforms the PC-like algorithm , and our modifications of the PC-like algorithm learn structures that are more similar to the underlying ground truth graphs than the original PC-like algorithm, especially in high-dimensional settings. In particular, we empirically show that the results of both algorithms are more accurate and stable when the sample size is reasonably large and the underlying graph is sparse.