Before revision:  Simulations under a variety of settings demonstrate the competitive performance of our decomposition-based method, called LCD-AMP, in comparison with the (modified version of) PC-like algorithm.
After revision:  We also extend the decomposition-based approach for learning Bayesian networks (BNs) proposed by (Xie et al., 2006) to learn AMP CGs, which include BNs as a special case, under the faithfulness assumption. We prove the correctness of our extension using the minimal separator results. Using standard benchmarks and synthetically generated models and data in our experiments demonstrate the competitive performance of our decomposition-based method, called LCD-AMP, in comparison with the (modified version of) PC-like algorithm.