On reduction integer programs to knapsack problem

Abstract

Let $A$ be an integral nonnegative $m\times n$ matrix, $b$ be an integral nonnegative vector. It is suggested new method for reduction of integer program $\max \{cx|Ax=b,x\ge 0,x\in {\mathbf{Z}}^n\}$ to knapsack problem $\max \{c^{\prime }x|fAx=fb,x\ge 0,x\in {\mathbf{Z}}^n\}$.