Learning Sparse Causal Models is not NP-hard
  This paper shows that causal model discovery is not an NP-hard problem, in
the sense that for sparse graphs bounded by node degree k the sound and
complete causal model can be obtained in worst case order N^{2(k+2)}
independence tests, even when latent variables and selection bias may be
present. We present a modification of the well-known FCI algorithm that
implements the method for an independence oracle, and suggest improvements for
sample/real-world data versions. It does not contradict any known hardness
results, and does not solve an NP-hard problem: it just proves that sparse
causal discovery is perhaps more complicated, but not as hard as learning
minimal Bayesian networks.
