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With the development of genome-wide association studies, how to gain information from a large scale of data has become an issue of common concern, since traditional methods are not fully developed to solve problems such as identifying loci-to-loci interactions (also known as epistasis). Previous epistatic studies mainly focused on local information with a single outcome (phenotype), while in this paper, we developed a two-stage global search algorithm, Greedy Equivalence Search with Local Modification (GESLM), to implement a global search of directed acycli