As standardly implemented in R or in the Tetrad program, causal search algorithms that have been most widely or effectively used in scientific problems have severe dimensionality constraints. However, implementation improvements are possible that extend the feasible dimensionality of search problems by several orders of magnitude. We describe optimizations for the Greedy Equivalence Search (GES) that allow search on 50,000 variable problems in 13 minutes for sparse models with 1000 samples, on a 4 processor 8G laptop computer, and in 18 hours for sparse models with 1000 samples on 1,000,000 variables on a supercomputer node at the Pittsburgh Supercomputing Center with 40 processors and 384 G RAM, on data generated i.i.d. from a linear, Gaussian model.