A note on non-degenerate integer programs with small sub-determinants

The intention of this note is two-fold. First, we study integer optimization problems in standard form defined by A∈Zm×nA∈Zm×n and find an algorithm to solve such problems in polynomial-time provided that both the largest absolute value of an entry in AA and mm are constant.Then, this is applied to solve integer programs in inequality form in polynomial-time, where the absolute values of all maximal sub-determinants of AA lie between 11 and a constant.