be ideal; developing such an algorithm is a direction for future work. Finally, despite Eagle's speed, its computational complexity contains a quadratic term (like all other published methods) and will become daunting for million-sample data sets. Most simply, this issue could be sidestepped by phasing very large samples in batches of a few hundred thousand samples at a time, but we expect that further algorithmic improvements will be possible, e.g., limiting the set of haplotypes considered as potential surrogate parents via clustering methods (as in SHAPEIT3; see URLs). Despite these limitations, we expect that Eagle in its current form—already much faster than existing methods with equal or better accuracy—will be a useful tool for large-sample phasing, and we believe further innovations will amplify the advantages of LRP-based phasing and imputation.
