Constraint satisfaction problems for first-order reducts of finitely bounded
homogeneous structures form a large class of computational problems that might
exhibit a complexity dichotomy, P versus NP-complete. A powerful method to
obtain polynomial-time tractability results for such CSPs is a certain
reduction to polynomial-time tractable finite-domain CSPs defined over k-types,
for a sufficiently large k. We give sufficient conditions when this method can
be applied and illustrate how to use the general results to prove a new
complexity dichotomy for first-order expansions of the basic relations of the
spatial reasoning formalism RCC5