  Discovering causal relationships from observational data is a crucial problem
and it has applications in many research areas. The PC algorithm is the
state-of-the-art constraint based method for causal discovery. However, runtime
of the PC algorithm, in the worst-case, is exponential to the number of nodes
(variables), and thus it is inefficient when being applied to high dimensional
data, e.g. gene expression datasets. On another note, the advancement of
computer hardware in the last decade has resulted in the widespread
availability of multi-core personal computers. There is a significant
motivation for designing a parallelised PC algorithm that is suitable for
personal computers and does not require end users' parallel computing knowledge
beyond their competency in using the PC algorithm. In this paper, we develop
parallel-PC, a fast and memory efficient PC algorithm using the parallel
computing technique. We apply our method to a range of synthetic and real-world
high dimensional datasets. Experimental results on a dataset from the DREAM 5
challenge show that the original PC algorithm could not produce any results
after running more than 24 hours; meanwhile, our parallel-PC algorithm managed
to finish within around 12 hours with a 4-core CPU computer, and less than 6
hours with a 8-core CPU computer. Furthermore, we integrate parallel-PC into a
causal inference method for inferring miRNA-mRNA regulatory relationships. The
experimental results show that parallel-PC helps improve both the efficiency
and accuracy of the causal inference algorithm.
