Solutions to the genotype-phenotype problem seek to identify the set of genetic mutations and interactions between them which modify risk for and severity of a trait of interest. I propose association graph reduction (AGR), a novel algorithm to detect such genetic lesions in genome-wide data, particularly in the presence of high-order interactions. I describe several existing methods and evaluate their performance in terms of computational cost and power to detect associations. An objective comparison of the results shows that AGR successfully combines high power with computational efficiency, while providing a detailed account of interactions present in the data. No other known method combines these three properties. When applied to real data, AGR can be used to discover genetic causes of common diseases such as arthritis, hypertension, diabetes, asthma, and many others, which will facilitate the discovery of novel diagnostic tools and treatment protocols
