The support of integer optimal solutions

The support of a vector is the number of nonzero-components. We show that given an integral m×n matrix A, the integer linear optimization problem max{cTx:Ax=b,x≥0,x∈Zn} has an optimal solution whose support is bounded by 2mlog(2m−−√∥A∥∞), where ∥A∥∞ is the largest absolute value of an entry of A. Compared to previous bounds, the one presented here is independent on the objective function. We furthermore provide a nearly matching asymptotic lower bound on the support of optimal solutions