  There has been an increasing interest in methods that exploit permutation
reasoning to search for directed acyclic causal models, including the "Ordering
Search" of Teyssier and Kohler and GSP of Solus, Wang and Uhler. We extend the
methods of the latter by a permutation-based operation, tuck, and develop a
class of algorithms, namely GRaSP, that are efficient and pointwise consistent
under increasingly weaker assumptions than faithfulness. The most relaxed form
of GRaSP outperforms many state-of-the-art causal search algorithms in
simulation, allowing efficient and accurate search even for dense graphs and
graphs with more than 100 variables.
