Experiment selection for causal discovery

Randomized controlled experiments are often described as the most reliable tool available to scientists discovering causal relationships among quantities of interest. However, it is often unclear many and which different experiments are needed to identify the full (possibly cyclic) causal among some given (possibly causally insufficient) set of variables. Recent results in the discovery literature have explored various identifiability criteria that depend on the assumptions is able to make about the underlying causal process, but these criteria are not directly for selecting the optimal set of experiments. Fortunately, many of the needed constructions exist in the combinatorics literature, albeit under terminology which is unfamiliar to of the causal discovery community. In this paper we translate the theoretical results and apply to the concrete problem of experiment selection. For a variety of settings we give explicit of the optimal set of experiments and adapt some of the general combinatorics results answer questions relating to the problem of experiment selection.