We have partially solved the ground state problem of binary alloys on the fcc lattice with pair interactions up to the fourth nearest neighbor distance. Our results extend the study presented by Kanamori and Kakehashi , releasing the constraint they imposed on the nearest neighbor correlation. The solution we present increases the number of possible ground state structures by an order of magnitude with respect to previous results. We have applied both the polyhedron and the enumeration method. The latter proved more powerful when including interactions beyond the second nearest neighbor distance.