Learning Bayesian network structure is one of the most exciting challenges in machine learning. Discovering a correct skeleton of a directed acyclic graph(DAG) is the foundation for dependency analysis algorithms for this problem. Considering the unreliability of high order condition independence(CI) tests, and to improve the efficiency of a dependency analysis algorithm, the key steps are to use few numbers of CI tests and reduce the sizes of conditioning sets as much as possible. Based on these reasons and inspired by the algorithm PC, we present an algorithm, named fast and efficient PC(FEPC), for learning the adjacent neighbourhood of every variable. FEPC implements the CI tests by three kinds of orders, which reduces the high order CI tests significantly. Compared with current algorithm proposals, the experiment results show that FEPC has better accuracy with fewer numbers of condition independence tests and smaller size of conditioning sets. The highest reduction percentage of CI test is 83.3% by EFPC compared with PC algorithm.
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