The paper discusses the application of the PC-algorithm for estimating the skeleton of a high-dimensional acyclic directed graph (DAG) with a Gaussian distribution. The PC-algorithm is computationally efficient for sparse DAGs with many nodes and automatically achieves high computational efficiency as the sparsity of the underlying DAG increases. The authors prove the consistency of the algorithm for very high-dimensional, sparse DAGs where the number of nodes can grow as fast as \(O(n^a)\) for any \(0 < a < \infty\). The sparsity assumption is minimal, requiring only that the neighborhoods in the DAG are of lower order than the sample size \(n\). Empirical results demonstrate that the PC-algorithm is insensitive to the choice of its tuning parameter, and it outperforms other methods like Greedy Equivalent Search (GES) and Maximum Weight Spanning Trees (MWST) in terms of True Discovery Rate (TDR) in simulated data. The PC-algorithm is shown to be computationally feasible even when the number of nodes is in the hundreds or thousands, making it a powerful tool for high-dimensional DAG estimation.The paper discusses the application of the PC-algorithm for estimating the skeleton of a high-dimensional acyclic directed graph (DAG) with a Gaussian distribution. The PC-algorithm is computationally efficient for sparse DAGs with many nodes and automatically achieves high computational efficiency as the sparsity of the underlying DAG increases. The authors prove the consistency of the algorithm for very high-dimensional, sparse DAGs where the number of nodes can grow as fast as \(O(n^a)\) for any \(0 < a < \infty\). The sparsity assumption is minimal, requiring only that the neighborhoods in the DAG are of lower order than the sample size \(n\). Empirical results demonstrate that the PC-algorithm is insensitive to the choice of its tuning parameter, and it outperforms other methods like Greedy Equivalent Search (GES) and Maximum Weight Spanning Trees (MWST) in terms of True Discovery Rate (TDR) in simulated data. The PC-algorithm is shown to be computationally feasible even when the number of nodes is in the hundreds or thousands, making it a powerful tool for high-dimensional DAG estimation.